Q: A $\$600$ investment earns $2.75\%$ interest compounded continuously for 5 years. What is the amount in the account after 5 years? Use $A = Pe^{rt}$.

$A = 600e^{0.0275 \times 5} \approx 688.44$

Question 1

Which of the following is the correct logarithmic form of the exponential equation $3^2 = 9$?

Accepted Answer

$\log_3 9 = 2$

Question 2

If $\log_b A = 2$ and $\log_b B = -5$, what is $\log_b (AB)$?

Accepted Answer

$-3$

Question 3

Which property of logarithms allows you to write $\log_a (xy) = \log_a x + \log_a y$?

Accepted Answer

Product Rule

Question 4

Solve for $x$: $3^x = 5$. (Round your answer to three decimal places.)

Accepted Answer

$x = \dfrac{\ln 5}{\ln 3} \approx 1.465$

Question 5

Which of the following is equivalent to $\log_{10} 1000$?

Accepted Answer

$3$

Question 6

If $P = 1000$, $r = 0.06$, $n = 4$, and $t = 5$, what is the compound amount $A$ after 5 years? Use $A = P \left(1 + \dfrac{r}{n}\right)^{nt}$.

Accepted Answer

$A = 1000 \left(1 + \dfrac{0.06}{4}\right)^{20} \approx 1348.85$

Question 7

Which of the following is the correct application of the change-of-base theorem for $\log_5 20$?

Accepted Answer

$\log_5 20 = \dfrac{\ln 20}{\ln 5}$

Question 8

A $\$600$ investment earns $2.75\%$ interest compounded continuously for 5 years. What is the amount in the account after 5 years? Use $A = Pe^{rt}$.

Accepted Answer

$A = 600e^{0.0275 	imes 5} \approx 688.44$

Question 9

Which of the following statements is true for all positive real numbers $a 
eq 1$?

Accepted Answer

$\log_a 1 = 0$

Question 10

Rewrite $7^x$ using base $e$ rather than base $7$.

Accepted Answer

$7^x = e^{x \ln 7}$

Question 11

Which property of logarithms allows you to write $\log_a \left(\dfrac{x}{y}\right) = \log_a x - \log_a y$?

Accepted Answer

Quotient Rule

Question 12

Evaluate $\ln(e^4)$.

Accepted Answer

$4$

Question 13

If $\log_2 x = 5$, what is the value of $x$?

Accepted Answer

$x = 32$

Question 14

Which of the following is equivalent to $\ln(1)$?

Accepted Answer

$0$

Question 15

Which of the following is the correct application of the power rule for logarithms?

Accepted Answer

$\log_a (x^r) = r \log_a x$

Question 16

A business invests $\$5,000$ at an annual interest rate of $4\%$ compounded quarterly. What is the amount after 10 years? Use $A = P \left(1 + \dfrac{r}{n}\right)^{nt}$.

Accepted Answer

$A = 5000 \left(1 + \dfrac{0.04}{4}\right)^{40} \approx 7,427.98$

Question 17

Which of the following is the correct exponential form of $\log_4 x = 3$?

Accepted Answer

$x = 4^3$

Question 18

If $\log_2 8 = x$, what is the value of $x$?

Accepted Answer

$3$

Question 19

Which of the following is a correct application of the properties of logarithms to simplify $\log_3 (x^2 y)$?

Accepted Answer

$2 \log_3 x + \log_3 y$

Exponential and Logarithmic Functions with Financial Applications

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