Q: Which of the following is the correct definition of an exponential function?

$f(x) = b^x$ where $b > 0$ and $b \neq 1$

Q: Which of the following statements about the graph of $f(x) = b^x$ for $0 < b < 1$ is true?

The function decreases rapidly as $x$ increases.

Q: Which of the following is the correct definition of a logarithmic function with base $a$?

$f(x) = \log_a x$ where $a > 0$ and $a \neq 1$

Question 1

Which of the following is the correct definition of an exponential function?

Accepted Answer

$f(x) = b^x$ where $b > 0$ and $b 
eq 1$

Question 2

Which of the following statements about the domain and range of the exponential function $f(x) = b^x$ (where $b > 0$ and $b 
eq 1$) is correct?

Accepted Answer

Domain: $x \in \mathbb{R}$, Range: $y > 0$

Question 3

Suppose a population of bacteria grows according to $N = N_0 e^{kt}$, where $N_0 = 25$ and $k = 1.386$. How many bacteria will there be after $t = 0.6$ hours? (Round to the nearest integer)

Accepted Answer

Approximately 57

Question 4

Which of the following is the correct formula for the amount $A$ in an account after $t$ years if $P$ is invested at an annual rate $r$ compounded $m$ times per year?

Accepted Answer

$A = P(1 + \frac{r}{m})^{mt}$

Question 5

A principal of $1,000$ is invested at $10\%$ annual interest compounded monthly for $10$ years. What is the future value $A$? (Use $A = P(1 + \frac{r}{m})^{mt}$)

Accepted Answer

$A \approx 2,707.04$

Question 6

Which of the following is the correct formula for continuous compound interest?

Accepted Answer

$A = Pe^{rt}$

Question 7

If $f(x) = 3^x$, what is $f(\sqrt{2})$?

Accepted Answer

$3^{\sqrt{2}} \approx 4.73$

Question 8

Which of the following statements about the graph of $f(x) = b^x$ for $0 < b < 1$ is true?

Accepted Answer

The function decreases rapidly as $x$ increases.

Question 9

Which of the following is the correct definition of a logarithmic function with base $a$?

Accepted Answer

$f(x) = \log_a x$ where $a > 0$ and $a 
eq 1$

Question 10

Convert the logarithmic equation $\log_3 x = 4$ to exponential form and solve for $x$.

Accepted Answer

$x = 81$

Question 11

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

Accepted Answer

Product Rule

Question 12

Expand the expression $\log_5 \left(\frac{x^2 y^3}{z}\right)$ using properties of logarithms.

Accepted Answer

$2\log_5 x + 3\log_5 y - \log_5 z$

Question 13

Which of the following is the correct change of base formula for logarithms?

Accepted Answer

$\log_a x = \frac{\log_b x}{\log_b a}$

Question 14

If $f(x) = \log_{10} x$, what is the value of $f(1000)$?

Accepted Answer

$f(1000) = 3$

Question 15

Which of the following is the correct inverse function of $f(x) = e^x$?

Accepted Answer

$f^{-1}(x) = \log_e x$

Question 16

Given the law of forgetting $\log P = \log P_0 - c \log(t + 1)$, if your initial score $P_0 = 90$, $c = 0.2$, and $t = 2$ months, what is your expected score $P$ after 2 months?

Accepted Answer

72

Question 17

Which of the following is the correct property of logarithms for $\log_a(x^r)$?

Accepted Answer

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

Question 18

If $f(x) = \log_2 x$, what is the domain and range of $f(x)$?

Accepted Answer

Domain: $x > 0$, Range: $y \in \mathbb{R}$

Question 19

A demand function for a product is given by $p = 3000 e^{-0.05q}$, where $q$ is the quantity demanded. What is the price per unit when $q = 15$?

Accepted Answer

$p \approx 406.01$

QMS110 Lecture 8

Study Guide - Practice Questions

Study Guide - Flashcards