Question 1

Which of the following best describes the main difference between linear and exponential models?

Accepted Answer

Linear models increase or decrease by a fixed amount, while exponential models increase or decrease by a fixed percentage.

Question 2

Suppose the Uber driver charges a flat rate of $$5 and 2 $$for every additional mile driven. Which equation models the total cost $$y as a $$function of miles driven $$x$$?

Accepted Answer

$$y = 2x + 5$$

Question 3

A company’s computer storage device doubles its capacity every two years. If it holds 16 TB today, how much will it hold in 6 years?

Accepted Answer

$$16 	imes 2^3$ = 128 TB$$

Question 4

Given the exponential model $$Q(t) = 100,000(1.60)^t$$ for COVID cases, where $$t is $$measured in 10-day increments, what is the predicted number of cases after 60 days?

Accepted Answer

$$Q(6) = 100,000(1.60)^6$ \approx 1,677,722$$

Question 5

Which of the following real-world phenomena is best modeled by an exponential function?

Accepted Answer

The depreciation of a car’s value by 10% each year.

Question 6

If the U.S. population in 2010 was 309 million and grows at 0.9% per year, which equation models the population $$Q(t)$$ years after 2010?

Accepted Answer

$$Q(t) = 309,000,000(1.009)^t$$

Question 7

A TV set costs $1000 today and its price decreases by 25% each year. What will the price be in 2 years?

Accepted Answer

$$1000(0.75)^2$$ = $$562.50$

Question 8

Which of the following is a defining property of a function?

Accepted Answer

Each input has one and only one output.

Question 9

The number of layers after tearing a sheet of paper $$x$$ times is given by $$y = 2^x. If $$you tear the paper 10 times, how many layers will you have?

Accepted Answer

$$2^{10} = 1024$

Question 10

A row of crops is planted such that the number of seeds per row is given by $$y = 0.25x$$, where $$x is $$the row length in feet. How many seeds can be planted in a row of 200 feet?

Accepted Answer

$$0.25 	imes 200 = 50$$

Question 11

Which of the following scenarios is best modeled by a linear function?

Accepted Answer

A school’s student population increases by 50 students each year.

Question 12

If China’s population in 2009 was 1.3 billion and declines at a rate of 0.5% per year, which equation models the population $$Q(t)$$ years after 2009?

Accepted Answer

$$Q(t) = 1,300,000,000(0.995)^t$$

Question 13

Which of the following best describes the growth of exponential functions?

Accepted Answer

They grow or decline slowly at first, then very rapidly.

Question 14

The death rate per 100,000 males as a function of hours of sleep is best modeled by which type of function?

Accepted Answer

Quadratic

Question 15

Which of the following is NOT a common application of exponential models?

Accepted Answer

The number of apples picked per hour at a constant rate.

Question 16

If a function is defined by $$f(x) = mx + b$$, what is the graph of this function?

Accepted Answer

A straight line

Linear and Exponential Models: Foundations and Applications

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