Real-Life Applications of Quadratic and Linear Functions

A ball is thrown upwards from a height of 2 meters. The height of the ball in meters after t seconds is given by the equation h(t) = -5t^2 + 10t + 2. What is the maximum height the ball reaches?

• 10 meters

• 7 meters

• 5 meters

• 3 meters

The cost of producing x items is given by the linear equation C(x) = 50x + 200. If the company wants to produce 100 items, what will be the total cost?

• 5100

• 5200

• 5400

• 5300

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 12 hours?

• 2000

• 8000

• 4000

• 10000

The path of a projectile can be modeled by the quadratic function h(t) = -4.9t^2 + 20t, where h is the height in meters and t is the time in seconds. How long will it take for the projectile to hit the ground?

• 2.5 seconds

• 6.0 seconds

• 3.2 seconds

• 4.08 seconds

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a linear equation to represent the total cost C for driving m miles. What is the cost for driving 150 miles?

• $60

• $30

• $90

• $120

The area A of a rectangle is given by the equation A = lw, where l is the length and w is the width. If the length is 3 meters more than the width, express the area as a quadratic function in terms of w. What is the area when w = 5 meters?

• 30 square meters

• 50 square meters

• 25 square meters

• 40 square meters

A certain investment grows according to the exponential function A(t) = 1000e^(0.05t), where A is the amount of money after t years. How much money will there be after 10 years?

• 1500.00

• 1648.72

• 2000.00

• 1200.50

The distance d in miles that a car travels is modeled by the linear equation d(t) = 60t, where t is the time in hours. How far will the car travel in 4 hours?

• 300 miles

• 120 miles

• 240 miles

• 180 miles

The height of a plant is modeled by the quadratic function h(t) = -t^2 + 4t + 1, where h is the height in centimeters and t is the time in weeks. What is the height of the plant after 2 weeks?

• 10 cm

• 5 cm

• 3 cm

• 7 cm

A store's sales can be modeled by the exponential function S(t) = 200(1.1)^t, where S is the sales in dollars and t is the time in years. What will the sales be after 5 years?

• 250.00

• 275.75

• 322.10

• 400.50