Q: If $$P = 500$$, $$r = 0.12$$, and $$t = 2$$, what is the future value using simple interest?

$$500 \times (1 + 0.12 \times 2)$$

Q: If $$P = 1000$$, $$r = 0.045$$, $$t = 5$$, and $$n = 4$$, what is the future value of the investment?

$$1000 \times (1 + \frac{0.045}{4}$$)^{20}$$

Q: A population of 8000 is expected to grow exponentially at a relative rate of 10% per year. What is the predicted population in 10 years?

$$8000 \times e$$^{0.1 \times 10}$$

Question 1

Suppose you deposit $0.01 on the first day of the month and double your deposit each day. What is the amount deposited on day 15?

Accepted Answer

$$0.01 	imes 2$$^{14}$$

Question 2

Which of the following best describes the function $$f(x) = a^x$$ where $$a \u003e 1$$?

Accepted Answer

It is an exponential function with constant base and variable exponent.

Question 3

Given the exponential decay formula $$Q(t) = Q_0$ 	imes 10$$^{\frac{-t}$${5715}}$$, what is the quantity of carbon-14 after 11,430 years if the initial quantity is 10 grams?

Accepted Answer

$$10 	imes 10$$^{-2}$$

Question 4

If $$P = 500$$, $$r = 0.12$$, and $$t = 2$$, what is the future value using simple interest?

Accepted Answer

$$500 	imes (1 + 0.12 	imes 2)$$

Question 5

Which formula gives the future value $$A of $$principal $$P at $$annual interest rate $$r$$ for $$t$$ years if interest is compounded $$n$$ times per year?

Accepted Answer

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

Question 6

If $$P = 1000$$, $$r = 0.045$$, $$t = 5$$, and $$n = 4$$, what is the future value of the investment?

Accepted Answer

$$1000 	imes (1 + \frac{0.045}{4}$$)^{20}$$

Question 7

What is the value of $$\lim_{n 	o \infty} \left(1 + \frac{1}{n}ight)^n$$?

Accepted Answer

$$e$$

Question 8

A population of 8000 is expected to grow exponentially at a relative rate of 10% per year. What is the predicted population in 10 years?

Accepted Answer

$$8000 	imes e$$^{0.1 	imes 10}$$

Question 9

If $$A = P e$$^{rt}$$, what does the variable r$ represent in the context of continuous compounding?

Accepted Answer

The annual interest rate

Question 10

Suppose you invest $1000 at 8% interest compounded annually. How long will it take to double your investment?

Accepted Answer

$$t = \frac{\log 2}{\log 1.08}$$

Question 11

Write $$81 = 3^x in $$logarithmic form.

Accepted Answer

$$x = \log_3$ 81$$

Question 12

Evaluate $$\log_5$ 25.$$

Accepted Answer

$$2$$

Question 13

Which of the following is the correct domain of the logarithmic function $$f(x) = \log_a x$$ for $$a \u003e 1$$?

Accepted Answer

$$(0, \infty)$$

Question 14

If $$f(x) = a^x$$ and $$g(x) = \log_a x$$, which statement is true?

Accepted Answer

$$f$$ and $$g$$ are inverses of each other.

Question 15

Which property is true for the exponential function $$f(x) = a^x$$ when $$0 \u003c a \u003c 1$$?

Accepted Answer

The function is decreasing.

Question 16

Convert the logarithmic equation $$\log_2$ x = 5 to $$exponential form.

Accepted Answer

$$x = 2^5$

Question 17

Which of the following is the horizontal asymptote of the exponential function $$f(x) = a^x$$?

Accepted Answer

$$y = 0$$

Question 18

If $$f(x) = 2^x$$ and $$g(x) = \log_2$ x$$, what is $$f(g(8))$$?

Accepted Answer

$$8$$

Question 19

Which of the following best describes the graph of $$y = \log_2$ x$$?

Accepted Answer

It passes through (1, 0) and increases slowly for large $$x.$$

Exponential and Logarithmic Functions: Precalculus Study Notes (MTH 161, Chapter 4)

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