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 $A = 20000 \left(1 + \frac{0.03}{12} ight)^{12 	imes 30}$)

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

Study Guide - Practice Questions

Study Guide - Flashcards