Real-Life Functions: Exponential Growth & Word Problems

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) as a function of miles driven (m). How much would it cost to drive 150 miles?

• $80

• $100

• $120

• $60

The height of a ball thrown into the air can be modeled by the quadratic function h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. What is the maximum height the ball reaches?

• 25 feet

• 18 feet

• 15 feet

• 21 feet

A population of bacteria doubles every 3 hours. If there are initially 500 bacteria, write an exponential function to model the population after t hours. How many bacteria will there be after 12 hours?

• 8000

• 4000

• 6000

• 10000

A store's sales can be modeled by the linear function S(x) = 200 + 15x, where S is the sales in dollars and x is the number of weeks since the store opened. What will the sales be after 10 weeks?

• 400

• 250

• 300

• 350

The area of a square garden increases as the length of its side increases. If the area A can be modeled by the function A(s) = s^2, where s is the length of a side, what is the area when the side length is 8 feet?

• 48 square feet

• 80 square feet

• 64 square feet

• 32 square feet

A car's value decreases exponentially over time. If the initial value of the car is $20,000 and it loses 15% of its value each year, write an exponential decay function to model its value after t years. What will the value be after 5 years?

• 12000.00

• 15000.00

• 10000.00

• 8874.00

The profit P from selling x items can be modeled by the quadratic function P(x) = -2x^2 + 40x - 100. What is the maximum profit, and how many items should be sold to achieve it?

• Maximum profit is 90, and 8 items should be sold.

• Maximum profit is 120, and 15 items should be sold.

• Maximum profit is 80, and 5 items should be sold.

• Maximum profit is 100, and 10 items should be sold.

A bank offers an account that compounds interest annually. If you deposit $1,000 at an interest rate of 5%, write an exponential function to model the amount A in the account after t years. How much will be in the account after 10 years?

• 1500.00

• 1628.89

• 1200.50

• 2000.00

The distance d (in miles) a cyclist travels can be modeled by the linear function d(t) = 12t, where t is the time in hours. How far will the cyclist travel in 4.5 hours?

• 48 miles

• 54 miles

• 36 miles

• 60 miles

A company's revenue R can be modeled by the quadratic function R(x) = -x^2 + 50x, where x is the number of units sold. What is the maximum revenue, and how many units should be sold to reach it?

• Maximum revenue is 625, and 25 units should be sold to reach it.

• Maximum revenue is 600, and 15 units should be sold to reach it.

• Maximum revenue is 700, and 30 units should be sold to reach it.

• Maximum revenue is 500, and 20 units should be sold to reach it.