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A table gives $x = 0, 1, 2, 3$ and $y = 4, 12, 36, 108$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 8 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 8, 24, 72, 216$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 16 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 7, 14, 28, 56$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 7 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 5, 15, 45, 135$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 10 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 5, 10, 20, 40$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 5 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 4, 20, 100, 500$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 16 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 2, 4, 8, 16$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 2 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 7, 28, 112, 448$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 21 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 2, 10, 50, 250$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 8 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 6, 30, 150, 750$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 24 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 4, 8, 16, 32$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 4 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 3, 15, 75, 375$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 12 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 8, 16, 32, 64$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 8 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 9, 18, 36, 72$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 9 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 5, 20, 80, 320$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 15 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 7, 35, 175, 875$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 28 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 3, 9, 27, 81$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 6 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 3, 6, 12, 24$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 3 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 7, 21, 63, 189$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 14 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 6, 12, 24, 48$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 2 at each step
2. Linear: $y$ goes up by 6 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 6, 24, 96, 384$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 18 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 9, 45, 225, 1125$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 36 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 4, 16, 64, 256$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 12 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 5, 25, 125, 625$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 20 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 2, 8, 32, 128$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 6 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 2, 6, 18, 54$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 4 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 9, 36, 144, 576$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 27 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 6, 18, 54, 162$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 12 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 8, 32, 128, 512$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 24 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 8, 40, 200, 1000$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 5 at each step
2. Linear: $y$ goes up by 32 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 9, 27, 81, 243$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 3 at each step
2. Linear: $y$ goes up by 18 at each step
3. Neither
A table gives $x = 0, 1, 2, 3$ and $y = 3, 12, 48, 192$ . What kind of relationship is it?
1. Exponential: $y$ is multiplied by 4 at each step
2. Linear: $y$ goes up by 9 at each step
3. Neither
An exponential function has $g(0) = 9$ and $g(1) = 18$ . Find $g(3)$ .
$f(x) = 57x + 380$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 73x + 397$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 27x + 452$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 41x + 461$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 90x + 394$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 71x + 341$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 70x + 452$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 48x + 332$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 37x + 394$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 82x + 296$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 47x + 267$ and $g(x) = 1.09^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 88x + 401$ and $g(x) = 1.06^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 79x + 459$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 72x + 433$ and $g(x) = 1.09^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 72x + 359$ and $g(x) = 1.06^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 43x + 245$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 20x + 184$ and $g(x) = 1.03^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 65x + 412$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 33x + 442$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 89x + 476$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 84x + 492$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 59x + 168$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 24x + 141$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 49x + 191$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 49x + 372$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 72x + 393$ and $g(x) = 1.06^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 69x + 378$ and $g(x) = 1.09^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 69x + 272$ and $g(x) = 1.03^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 37x + 373$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 68x + 122$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 85x + 375$ and $g(x) = 1.03^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 86x + 451$ and $g(x) = 1.03^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 47x + 464$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 41x + 149$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 22x + 463$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 36x + 450$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 66x + 237$ and $g(x) = 1.08^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 33x + 387$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 43x + 145$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 75x + 433$ and $g(x) = 1.09^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 35x + 196$ and $g(x) = 1.09^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 81x + 370$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 63x + 195$ and $g(x) = 1.07^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 74x + 280$ and $g(x) = 1.07^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 37x + 189$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 52x + 272$ and $g(x) = 1.02^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 22x + 228$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 77x + 450$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 86x + 253$ and $g(x) = 1.05^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
$f(x) = 70x + 179$ and $g(x) = 1.04^x$ . For very large $x$ , which is greater?
1. $g$ : exponential growth eventually overtakes linear growth
2. $f$ : it is greater now and grows faster
3. They stay about equal
An arithmetic sequence has $a_1 = 14$ and common difference 2. Find $a_{ 43 }$ .
In an arithmetic sequence, $a_{ 4 } = 28$ and $a_{ 9 } = 68$ . Find the common difference.
What kind of sequence is $3, 6, 12, 24, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $1, 2, 4, 8, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $3, 12, 48, 192, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $3, 9, 27, 81, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 8, 16, 32, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 8, 32, 128, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $4, 12, 36, 108, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $1, 4, 16, 64, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $5, 20, 80, 320, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $2, 4, 8, 16, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $5, 15, 45, 135, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $5, 10, 20, 40, \dots$ ?
1. Geometric, with ratio 2
2. Arithmetic
3. Neither
What kind of sequence is $2, 6, 18, 54, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
What kind of sequence is $4, 16, 64, 256, \dots$ ?
1. Geometric, with ratio 4
2. Arithmetic
3. Neither
What kind of sequence is $1, 3, 9, 27, \dots$ ?
1. Geometric, with ratio 3
2. Arithmetic
3. Neither
A geometric sequence has $a_1 = 3$ and ratio 3. Find $a_{ 4 }$ .
Find the common ratio of the geometric sequence $8, 32, 128, \dots$
Write a formula for $a_n$ , starting at $n = 1$ : $2, 8, 32, \dots$
Evaluate $36^{ \frac{ 5 }{2} }$ .
Evaluate $125^{ -\frac{ 2 }{3} }$ .
A culture starts with 7 grams of algae. Each week, the amount is multiplied by 3. How many grams are there after 3 weeks?
A photo is 8000 pixels wide. Each time it is resized, its width loses 40%. Write the width $W(t)$ after $t$ resizes.
The amount of algae starts at 5 m² and is multiplied by 4 each week. Complete the table.
$f(x) = 24 \cdot 4^x$ . Find $f(-1)$ .
Is $f(x) = 4 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 4 is greater than 1
3. A linear decrease
Is $f(x) = 10 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 10 is greater than 1
3. A linear decrease
Is $f(x) = 20 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 20 is greater than 1
3. A linear decrease
Is $f(x) = 22 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 22 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 12 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 12 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 25 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 25 is greater than 1
3. A linear decrease
Is $f(x) = 5 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 5 is greater than 1
3. A linear decrease
Is $f(x) = 10 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 10 is greater than 1
3. A linear decrease
Is $f(x) = 43 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 43 is greater than 1
3. A linear decrease
Is $f(x) = 17 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 17 is greater than 1
3. A linear decrease
Is $f(x) = 39 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 39 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 16 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 16 is greater than 1
3. A linear decrease
Is $f(x) = 35 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 35 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 50 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 50 is greater than 1
3. A linear decrease
Is $f(x) = 32 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 32 is greater than 1
3. A linear decrease
Is $f(x) = 19 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 19 is greater than 1
3. A linear decrease
Is $f(x) = 4 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 4 is greater than 1
3. A linear decrease
Is $f(x) = 37 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 37 is greater than 1
3. A linear decrease
Is $f(x) = 26 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 26 is greater than 1
3. A linear decrease
Is $f(x) = 14 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 14 is greater than 1
3. A linear decrease
Is $f(x) = 9 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 9 is greater than 1
3. A linear decrease
Is $f(x) = 3 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 3 is greater than 1
3. A linear decrease
Is $f(x) = 41 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 41 is greater than 1
3. A linear decrease
Is $f(x) = 28 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 28 is greater than 1
3. A linear decrease
Is $f(x) = 41 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 41 is greater than 1
3. A linear decrease
Is $f(x) = 13 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 13 is greater than 1
3. A linear decrease
Is $f(x) = 49 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 49 is greater than 1
3. A linear decrease
Is $f(x) = 7 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 7 is greater than 1
3. A linear decrease
Is $f(x) = 49 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 49 is greater than 1
3. A linear decrease
Is $f(x) = 44 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 44 is greater than 1
3. A linear decrease
Is $f(x) = 29 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 29 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 25 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 25 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 46 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 46 is greater than 1
3. A linear decrease
Is $f(x) = 28 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 28 is greater than 1
3. A linear decrease
Is $f(x) = 47 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 47 is greater than 1
3. A linear decrease
Is $f(x) = 15 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 15 is greater than 1
3. A linear decrease
Is $f(x) = 35 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 35 is greater than 1
3. A linear decrease
Is $f(x) = 11 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 11 is greater than 1
3. A linear decrease
Is $f(x) = 33 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 33 is greater than 1
3. A linear decrease
Is $f(x) = 24 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 24 is greater than 1
3. A linear decrease
Is $f(x) = 43 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 43 is greater than 1
3. A linear decrease
Is $f(x) = 31 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 31 is greater than 1
3. A linear decrease
Is $f(x) = 24 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 24 is greater than 1
3. A linear decrease
Is $f(x) = 23 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 23 is greater than 1
3. A linear decrease
The graph of an exponential function passes through $(0, 8)$ and $(1, 16)$ . Write $f(x)$ .
An exponential function $f$ has $f(0) = 9$ , and each time $x$ increases by 1, the value of $f$ is multiplied by 5. Write $f(x)$ .
A population is 7 thousand at $t = 0$ and is multiplied by 3 every 4 years. Write the population $P(t)$ , in thousands, after $t$ years.
Plot the points of the graph of $f(x) = 4 \cdot 2^x$ at $x = 0$ and $x = 1$ .
A quantity grows by 9% each year. By what number is it multiplied each year (the growth factor)?
882 dollars are invested at 5% per year, compounded yearly. Write the value after 4 years (an exact expression is fine).
660 dollars are invested at 4% per year, compounded monthly. Write the value after 2 years (an exact expression is fine).

Answers

Exponential: $y$ is multiplied by 3 at each step
$72$
$g$ : exponential growth eventually overtakes linear growth
$98$
$8$
Geometric, with ratio 2
$81$
$4$
$2 \cdot 4^{n - 1}$
$7776$
$\frac{1}{25}$
$189$
$8000 \left(\frac{3}{5}\right)^{t}$
$20, 80, 320$
$6$
Decay: each step multiplies by $\tfrac{1}{ 4 }$
$8 \cdot 2^{x}$
$9 \cdot 5^{x}$
$7 \cdot 3^{\frac{t}{4}}$
$(0, 4),\ (1, 8)$
$\frac{109}{100}$
$\frac{85766121}{80000}$
$\frac{3365027202877485792030412063535621133822430265203298001319211}{4707158941350000000000000000000000000000000000000000000000}$