Question 1

Suppose you invest $$20,000 in a bank account that compounds interest monthly at an annual rate of 3%. Which formula correctly models the total amount A$ in the account after t$ years?

Accepted Answer

$$A = 20000 \left(1 + \frac{0.03}{12} \$$right)^{12t}$$

Question 2

If you want your $$20,000 investment to triple in value in an account that compounds monthly at 3% annual interest, which equation would you solve for t$?

Accepted Answer

$$60000 = 20000 \left(1 + \frac{0.03}{12} \$$right)^{12t}$$

Question 3

Given the function $$f(x) = x^2$ - 1$$ with domain $$x \geq 0$$, what is the correct expression for its inverse $$g(x)$$?

Accepted Answer

$$g(x) = \sqrt{x + 1}$$

Question 4

What is the domain of the function $$f(x) = x^2$ - 1$$ where $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 5

What is the range of the function $$f(x) = x^2$ - 1$$ for $$x \geq 0$$?

Accepted Answer

$$[-1, \infty)$$

Question 6

What is the domain of the inverse function $$g(x) = \sqrt{x + 1}$$?

Accepted Answer

$$x \geq -1$$

Question 7

What is the range of the inverse function $$g(x) = \sqrt{x + 1}$$?

Accepted Answer

$$[0, \infty)$$

Question 8

If you invest $$20,000 at 3$$% annual interest compounded monthly, approximately how many years will it take for your investment to triple? (Round to the nearest year.)

Accepted Answer

Approximately 37 years

Question 9

Which of the following steps is necessary to verify that $$g(x) is $$the inverse of $$f(x)$$, where $$f(x) = x^2$ - 1$$ and $$g(x) = \sqrt{x + 1}$$?

Accepted Answer

Show that $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 10

A medical research fund invests $$20,000 at 3$$% annual interest compounded monthly. If the fund needs at least $$50,000 in 30 $$years, will the investment be sufficient? (Use $$A = 20000 \left(1 + \frac{0.03}{12} \$$right)^{12 	imes 30}$$)

Accepted Answer

No, because the final amount will be less than $$50,000$$

Question 11

Suppose you want to solve for $$t in $$the equation $$3 = \left(1 + \frac{0.03}{12} \$$right)^{12t}$$. Which mathematical operation should you use first?

Accepted Answer

Take the natural logarithm of both sides

Question 12

A chemical company needs to quadruple its $$20,000$$ investment in a research fund that compounds monthly at 3% annual interest. Which equation should they solve for $$t$$?

Accepted Answer

$$80000 = 20000 \left(1 + \frac{0.03}{12} \$$right)^{12t}$$

Question 13

If $$f(x) = x^2$ - 1$$ for $$x \geq 0$$, what is $$f(g(x))$$ where $$g(x) = \sqrt{x + 1}$$?

Accepted Answer

$$x$$

Question 14

A student claims that the inverse of $$f(x) = x^2$ - 1 is$$ $$g(x) = x^2$ + 1. $$Which of the following best explains why this is incorrect?

Accepted Answer

Because the inverse should undo the original function, and $$g(x) = x^2$ + 1$$ does not satisfy $$f(g(x)) = x$$

Question 15

If you invest $$20,000 at 3$$% annual interest compounded monthly, what is the value of $$A$$ after 10 years? (Round to the nearest dollar.)

Accepted Answer

$$26,897$$

Question 16

Which of the following best describes the relationship between a function and its inverse?

Accepted Answer

The function and its inverse undo each other, so $$f(g(x)) = x$$ and $$g(f(x)) = x$$

College Algebra Study Notes: Compound Interest and Inverse Functions

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