1. Functions and Modeling

Exponential Models — Quiz

Test your understanding of exponential models with 5 practice questions.

Practice Questions

Question 1

An investment of 5000 is placed into an account that earns interest compounded continuously at an annual rate of 4.5%. What is the value of the investment after 7 years? (Use the formula for continuous compounding: $A = P e^{rt}$)

Question 2

A population of bacteria is modeled by the function $P(t) = 2000 \times 3^{0.5t}$, where $t$ is in hours. How many hours will it take for the population to reach 18,000?

Question 3

The half-life of a certain radioactive substance is 6 years. If the initial amount is 80 grams, which of the following functions best models the amount remaining after $t$ years?

Question 4

A certain quantity is growing according to the model $Q(t) = 250 \times e^{0.08t}$. At what time $t$ will the quantity double?

Question 5

The function $f(x) = 5 \times 2^{3x - 4}$ represents an exponential growth. What is the value of $f(3)$?