Modeling Real-Life Situations with Functions and Transformations

A car rental company charges a flat fee of $50 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?

• 100

• 120

• 60

• 80

A gardener is planting a rectangular garden. The length of the garden is twice the width. If the area of the garden is 200 square feet, write a quadratic equation to find the dimensions of the garden. What are the dimensions?

• Width: 5 feet, Length: 10 feet

• Width: 15 feet, Length: 30 feet

• Width: 10 feet, Length: 20 feet

• Width: 8 feet, Length: 16 feet

The population of a small town can be modeled by the function P(t) = 500(1.03)^t, where t is the number of years since 2020. How many people will live in the town in 2025?

• 500

• 580

• 550

• 600

A ball is thrown upwards from a height of 5 feet with an initial velocity of 20 feet per second. The height of the ball (h) after t seconds can be modeled by the equation h(t) = -16t^2 + 20t + 5. What is the maximum height reached by the ball?

• 12 feet

• 15 feet

• 11.25 feet

• 10 feet

A company's profit 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 sold that maximizes the profit.

• 3

• 5

• 2

• 4

The cost of producing x items is given by the function C(x) = 3x^2 + 12x + 100. What is the minimum cost of production, and at what number of items produced does this occur?

• Minimum cost is 150 at 5 items produced.

• Minimum cost is 120 at 10 items produced.

• Minimum cost is 100 at 0 items produced.

• Minimum cost is 90 at 2 items produced.

A scientist is studying the growth of bacteria in a lab. The number of bacteria can be modeled by the function N(t) = 100e^(0.5t), where t is time in hours. How many bacteria will there be after 4 hours?

• 739

• 1000

• 300

• 500

A rectangular swimming pool has a length that is 3 feet longer than its width. If the area of the pool is 150 square feet, write a quadratic equation to find the dimensions of the pool. What are the dimensions?

• Width: 10 feet, Length: 13 feet

• Width: 5 feet, Length: 8 feet

• Width: 8 feet, Length: 11 feet

• Width: 12 feet, Length: 15 feet

The height of a projectile launched from the ground can be modeled by the equation h(t) = -16t^2 + 64t, where t is time in seconds. How long will it take for the projectile to hit the ground?

• 8 seconds

• 4 seconds

• 6 seconds

• 2 seconds

A store's sales can be modeled by the function S(t) = 200 + 50t, where t is the number of months since the store opened. If the store opened 6 months ago, what are the current sales?

• 600

• 300

• 500

• 400