Q: Suppose you invest \$10,000 in an account that earns 5\% annual interest compounded monthly. What will the balance be after 8 years? Use the formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$.

$A = 10,000 \left(1 + \frac{0.05}{12}\right)^{12 \times 8} \approx 14,859$

Question 1

Suppose you invest \$10,000 in an account that earns 5\% annual interest compounded monthly. What will the balance be after 8 years? Use the formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$.

Accepted Answer

$A = 10,000 \left(1 + \frac{0.05}{12}ight)^{12 	imes 8} \approx 14,859$

Question 2

Solve for $x$: $e^{2x} = 7$.

Accepted Answer

$x = \frac{1}{2} \ln 7$

Question 3

A radioactive substance decays according to $A = A_0 e^{-kt}$. If a sample has a half-life of 20 years, what is the value of $k$?

Accepted Answer

$k = \frac{\ln 2}{20}$

Question 4

Which of the following is equivalent to $\ln(e^{3x})$?

Accepted Answer

$3x$

Question 5

If $\log_{b} 8 = 3$, what is the value of $b$?

Accepted Answer

$b = 2$

Question 6

A population grows exponentially according to $P(t) = 5000 e^{0.03t}$. What is the population after 10 years?

Accepted Answer

$P(10) = 5000 e^{0.3} \approx 6749$

Question 7

Solve for $x$: $\ln(x - 2) = 3$.

Accepted Answer

$x = e^{3} + 2$

Question 8

Which of the following is the solution to $2^{x} = 10$?

Accepted Answer

$x = \log_{2} 10$

Question 9

If $A = P e^{rt}$, how long will it take for an investment to double if the interest rate is 6\% compounded continuously?

Accepted Answer

$t = \frac{\ln 2}{0.06}$

Question 10

Which of the following is the inverse function of $f(x) = e^{x}$?

Accepted Answer

$f^{-1}(x) = \ln x$

Question 11

A medication is eliminated from the bloodstream at a rate proportional to the amount present. If the half-life is 4 hours, what fraction remains after 12 hours?

Accepted Answer

$\left(\frac{1}{2}\right)^{3} = \frac{1}{8}$

Question 12

If $\log_{10} x = 2$, what is $x$?

Accepted Answer

$x = 100$

Question 13

Which of the following expressions is equivalent to $\log_{a}(xy)$?

Accepted Answer

$\log_{a} x + \log_{a} y$

Question 14

A car depreciates at a rate of 12\% per year. If the car is currently worth \$20,000, what will it be worth in 5 years? Use $A = P(1 - r)^{t}$.

Accepted Answer

$A = 20,000 (0.88)^{5} \approx 10,747$

Question 15

Solve for $x$: $3^{2x-1} = 27$.

Accepted Answer

$x = 2$

Question 16

Which of the following is the correct formula for the amount $A$ after $t$ years for an initial principal $P$ at an annual interest rate $r$ compounded $n$ times per year?

Accepted Answer

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Question 17

If $\log_{b} 81 = 4$, what is $b$?

Accepted Answer

$b = 3$

Question 18

A scientist starts with 100 grams of a substance that decays at a rate of 7\% per year. How much remains after 10 years? Use $A = P(1 - r)^{t}$.

Accepted Answer

$A = 100 (0.93)^{10} \approx 48.1$

Question 19

Which of the following is equivalent to $\log_{a} \left(\frac{x}{y}\right)$?

Accepted Answer

$\log_{a} x - \log_{a} y$

Question 20

If $f(x) = \ln(x)$, what is the domain of $f$?

Accepted Answer

$(0, \infty)$

Exponential and Logarithmic Functions: Applications in Finance and Growth

Study Guide - Practice Questions

Study Guide - Flashcards