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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