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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 $f(x)$ .
Evaluate $36^{ \frac{ 5 }{2} }$ .
Evaluate $125^{ -\frac{ 2 }{3} }$ .
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 $x = 1$ .
Evaluate $\log_{ 4 } 16$ .
Solve $6^x = 21$ . Write the exact answer using a logarithm.
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 8 } y = 2$
2. $\log_{ 8 } y = 3$
3. $\log_{ 8 } y = -1$
4. $\log_{ 8 } y = \tfrac{1}{2}$
1. $y = 8^{2}$
2. $y = 8^{3}$
3. $y = \dfrac{1}{ 8 }$
4. $y = \sqrt{ 8 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 3 } y = 2$
2. $\log_{ 3 } y = 3$
3. $\log_{ 3 } y = -1$
4. $\log_{ 3 } y = \tfrac{1}{2}$
1. $y = 3^{2}$
2. $y = 3^{3}$
3. $y = \dfrac{1}{ 3 }$
4. $y = \sqrt{ 3 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 4 } y = 2$
2. $\log_{ 4 } y = 3$
3. $\log_{ 4 } y = -1$
4. $\log_{ 4 } y = \tfrac{1}{2}$
1. $y = 4^{2}$
2. $y = 4^{3}$
3. $y = \dfrac{1}{ 4 }$
4. $y = \sqrt{ 4 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 6 } y = 2$
2. $\log_{ 6 } y = 3$
3. $\log_{ 6 } y = -1$
4. $\log_{ 6 } y = \tfrac{1}{2}$
1. $y = 6^{2}$
2. $y = 6^{3}$
3. $y = \dfrac{1}{ 6 }$
4. $y = \sqrt{ 6 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 2 } y = 2$
2. $\log_{ 2 } y = 3$
3. $\log_{ 2 } y = -1$
4. $\log_{ 2 } y = \tfrac{1}{2}$
1. $y = 2^{2}$
2. $y = 2^{3}$
3. $y = \dfrac{1}{ 2 }$
4. $y = \sqrt{ 2 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 9 } y = 2$
2. $\log_{ 9 } y = 3$
3. $\log_{ 9 } y = -1$
4. $\log_{ 9 } y = \tfrac{1}{2}$
1. $y = 9^{2}$
2. $y = 9^{3}$
3. $y = \dfrac{1}{ 9 }$
4. $y = \sqrt{ 9 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 5 } y = 2$
2. $\log_{ 5 } y = 3$
3. $\log_{ 5 } y = -1$
4. $\log_{ 5 } y = \tfrac{1}{2}$
1. $y = 5^{2}$
2. $y = 5^{3}$
3. $y = \dfrac{1}{ 5 }$
4. $y = \sqrt{ 5 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 7 } y = 2$
2. $\log_{ 7 } y = 3$
3. $\log_{ 7 } y = -1$
4. $\log_{ 7 } y = \tfrac{1}{2}$
1. $y = 7^{2}$
2. $y = 7^{3}$
3. $y = \dfrac{1}{ 7 }$
4. $y = \sqrt{ 7 }$
An account holds 400 dollars and grows continuously at 3% per year. Write the amount $A(t)$ after $t$ years.
The area of mold is $f(t) = 2e^{ 4t }$ square millimetres after $t$ days. By what factor is the area multiplied each day? Give the exact value.
Solve $e^{ 5x } = 25$ .
Solve $e^{ 4x + 4 } = 12$ .
Solve $3e^{ 4x } + 6 = 60$ .
The graph of $y = \log_b x$ passes through the point $(9, 2)$ . What is $b$ ?
Where does the graph of $y = \ln(x - 3)$ cross the $x$ -axis? Give the value of $x$ .
What is the domain of $y = \ln(x - 6)$ ? Give it as an interval.
Here is the graph of $y = \log_{ 3 }(x - 5)$ . Tap the point where it crosses the $x$ -axis.

Answers

$189$
$8000 \left(\frac{3}{5}\right)^{t}$
$20, 80, 320$
$6$
Decay: each step multiplies by $\tfrac{1}{ 4 }$
$8 \cdot 2^{x}$
$7776$
$\frac{1}{25}$
$9 \cdot 5^{x}$
$7 \cdot 3^{\frac{t}{4}}$
$(0, 4),\ (1, 8)$
$2$
$\frac{\ln{\left(21 \right)}}{\ln{\left(6 \right)}}$
$\log_{ 8 } y = 2$ → $y = 8^{2}$ · $\log_{ 8 } y = 3$ → $y = 8^{3}$ · $\log_{ 8 } y = -1$ → $y = \dfrac{1}{ 8 }$ · $\log_{ 8 } y = \tfrac{1}{2}$ → $y = \sqrt{ 8 }$
$400 e^{\frac{3 t}{100}}$
$e^{4}$
$\frac{\ln{\left(25 \right)}}{5}$
$-1 + \frac{\ln{\left(12 \right)}}{4}$
$\frac{\ln{\left(18 \right)}}{4}$
$3$
$4$
$(6, \infty)$
$(6, 0)$