Modeling Real-World Functions: A 9th Grade Challenge

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a linear function to model the total cost (C) based on the number of miles (m) driven. What is the cost for driving 150 miles?

• 60

• 50

• 80

• 100

A ball is thrown upwards from a height of 5 feet with an initial velocity of 20 feet per second. The height (h) of the ball after t seconds can be modeled by the equation h(t) = -16t^2 + 20t + 5. How long will it take for the ball to hit the ground?

• 1.25 seconds

• 3.00 seconds

• 2.50 seconds

• 1.79 seconds

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

• 10000

• 6000

• 4000

• 8000

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

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

• Width: 7 meters, Length: 10 meters

A store is having a sale where the price of a jacket is reduced by 25% from its original price of $80. Write a linear function to model the sale price (S) based on the original price (P). What is the sale price of the jacket?

• $40

• $60

• $70

• $50

The height of a projectile launched from the ground can be modeled by the equation h(t) = -16t^2 + 64t, where h is the height in feet and t is the time in seconds. At what time does the projectile reach its maximum height?

• 4 seconds

• 3 seconds

• 1 second

• 2 seconds

A company’s profit (P) can be modeled by the function P(x) = -2x^2 + 12x - 10, where x is the number of units sold. Determine the number of units that must be sold to maximize profit.

• 3

• 4

• 2

• 5

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

• $15,000.00

• $12,000.00

• $8,874.00

• $5,000.00

A farmer has a rectangular field with a perimeter of 100 meters. If the length is twice the width, write a quadratic equation to find the dimensions of the field. What are the dimensions?

• Width: 10 meters, Length: 30 meters

• Width: 16.67 meters, Length: 33.33 meters

• Width: 20 meters, Length: 40 meters

• Width: 25 meters, Length: 50 meters

A local gym charges a monthly fee of $40 plus $10 for each class attended. Write a linear function to model the total cost (C) based on the number of classes (c) attended. How much will it cost to attend 8 classes?

• $140

• $120

• $80

• $100