Unit 5 test: Exponential and Logarithmic Functions

The function $f(x) = 3(0.75)^x$ shows exponential decay. By what percent does $f(x)$ decrease each time $x$ increases by $1$?

An exponential function $f(x) = a \cdot b^x$ passes through $(1, 6)$ and $(3, 54)$. Find $f(4)$.

You invest $4,000 at $5\%$ interest compounded continuously. What is the balance after $8$ years? Round to the nearest cent.

Evaluate $\log_2 \dfrac{1}{32}$.

Evaluate $\log_{16} 8$.

Find the domain of $f(x) = \ln(5 - x)$.

Which is the expanded form of $\ln \dfrac{x^4\sqrt{y}}{z}$?

If $\log_b 5 = 1.2$ and $\log_b 2 = 0.5$, find $\log_b 50$.

Evaluate $\log_7 50$. Round to $3$ decimal places.

Solve $27^x = 9^{x + 2}$.

Solve $5e^{2x} = 60$. Round to $3$ decimal places.

Solve $\log_3(x + 2) + \log_3(x - 4) = 3$.

Solve $\ln(2x - 1) = 4$. Round to $3$ decimal places.

A medication has a half-life of $12$ hours. How many hours does it take a $200$ mg dose to decrease to $30$ mg? Round to $2$ decimal places.

A town grows from $8000$ to $11{,}000$ people in $4$ years. Using the model $P = 8000e^{kt}$, find the continuous growth rate $k$. Round to $4$ decimal places.