Question 1

Which of the following best describes the 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 an Uber driver charges a flat rate of $$5 plus 2 $$for every 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 revenue is modeled by $$y = 50,000x + 1,000,000$$, where $$x is $$the number of employees hired since 2017. What is the projected revenue if the company has hired 70 employees since 2017?

Accepted Answer

$$y = 4,500,000$$

Question 4

Given the function $$y = 0.25x$$ representing seeds per row as a function of row length $$x in $$feet, how many seeds can be planted in a row of 200 feet?

Accepted Answer

$$50$$

Question 5

Which of the following equations best models the number of paper layers after $$x$$ tears, starting with one sheet?

Accepted Answer

$$y = 2^x$$

Question 6

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

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 two years?

Accepted Answer

$$562.50$$

Question 8

Which of the following scenarios is best modeled by an exponential function?

Accepted Answer

A bank account that earns 5% interest compounded annually.

Question 9

The memory capacity of a computer drive doubles every two years. If the current capacity is 16 TB, what will it be in six years?

Accepted Answer

$$128 TB$$

Question 10

Which of the following best describes why the death rate data as a function of hours of sleep is quadratic?

Accepted Answer

The death rate first decreases, reaches a minimum, and then increases, forming a parabola.

Question 11

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

Accepted Answer

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

Question 12

A school’s student population increases by 50 students each year. If there were 1700 students four years ago, what is the population today?

Accepted Answer

$$1900$$

Question 13

Which of the following is a key feature of exponential growth compared to linear growth?

Accepted Answer

Exponential growth multiplies by a fixed factor each period.

Question 14

If the number of COVID cases in the U.S. increases by 60% every 10 days, starting from 100,000 cases, what is the equation for the number of cases after $$t$$ periods of 10 days?

Accepted Answer

$$Q(t) = 100,000(1.6)^t$$

Question 15

Which of the following is NOT a typical real-world application of exponential models?

Accepted Answer

Linear depreciation of a car

Question 16

Which of the following statements about functions is correct?

Accepted Answer

A function assigns exactly one output to each input.

Linear and Exponential Models: Functions, Graphs, and Applications

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