Real-Life Functions: Solving Exponential Models & More

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) = -4.9t^2 + 2. Find the time when the ball hits the ground.

• 1.00 seconds

• 0.64 seconds

• 0.32 seconds

• 1.28 seconds

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 of renting a car for m miles. How much would it cost to drive 150 miles?

• $100

• $60

• $80

• $120

The population of a small town is modeled by the equation P(t) = 500e^(0.03t), where t is the number of years since 2020. What will the population be in 5 years?

• 550

• 500

• 581

• 600

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 54 square meters, find the dimensions of the garden using a quadratic equation.

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

The value of a car decreases exponentially over time. If a car is worth $20,000 when new and loses 15% of its value each year, what will its value be after 3 years?

• $15,000.00

• $10,000.00

• $18,000.00

• $12,282.50

A store sells a product for $30, and the price increases by 10% each year. Write an exponential function to model the price after t years. What will the price be after 4 years?

• $36.00

• $50.00

• $40.00

• $43.92

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. Determine the maximum height reached by the projectile and the time it takes to reach that height.

• Maximum height: 160 feet, Time to reach maximum height: 1 second

• Maximum height: 144 feet, Time to reach maximum height: 2 seconds

• Maximum height: 100 feet, Time to reach maximum height: 4 seconds

• Maximum height: 128 feet, Time to reach maximum height: 3 seconds

A local gym charges a monthly fee of $25 plus $10 for each class attended. Write a linear equation for the total cost C for attending c classes in a month. How much would it cost if a member attends 8 classes?

• $105

• $95

• $120

• $85

The number of bacteria in a culture doubles every 3 hours. If there are initially 500 bacteria, write an exponential function to model the growth. How many bacteria will there be after 12 hours?

• 4000

• 2000

• 10000

• 8000

A farmer has a rectangular field with a perimeter of 100 meters. If the length is twice the width, find the dimensions of the field using a quadratic equation.

• Width: 20 meters, Length: 40 meters

• Width: 25 meters, Length: 50 meters

• Width: 10 meters, Length: 20 meters

• Width: 16.67 meters, Length: 33.33 meters