Radical Functions: Exploring Graphs and Applications

A gardener is designing a circular flower bed with a radius of 4 feet. If the area of the flower bed is represented by the function A(r) = πr², how can you express the radius in terms of the area?

• r = A/π

• r = πA

• r = √(A/π)

• r = 4A

A car's speed is modeled by the function s(t) = √(t + 1), where s is the speed in meters per second and t is the time in seconds. What is the speed of the car after 3 seconds?

• 2 meters per second

• 4 meters per second

• 3 meters per second

• 1 meter per second

The height of a ball thrown into the air can be modeled by the function h(t) = -16t² + 64, where h is the height in feet and t is the time in seconds. At what time does the ball reach a height of 48 feet?

• 1 second

• 0.5 seconds

• 2 seconds

• 3 seconds

A swimming pool is being filled with water at a rate that can be modeled by the function V(t) = 5√t, where V is the volume in cubic feet and t is the time in minutes. How long will it take to fill the pool to a volume of 80 cubic feet?

• 120 minutes

• 180 minutes

• 256 minutes

• 300 minutes

The distance d in miles that a car can travel on a certain amount of gas can be modeled by the function d(g) = 3√g, where g is the gallons of gas. If the car has 8 gallons of gas, how far can it travel?

• 10 miles

• 8.49 miles

• 5.5 miles

• 12 miles

A rectangular garden has a length that is 3 feet longer than its width. If the area of the garden is represented by the function A(w) = w(w + 3), where w is the width, what is the width if the area is 40 square feet?

• 6 feet

• 4 feet

• 5 feet

• 7 feet

The time it takes for a ball to hit the ground can be modeled by the function t(h) = √(h/16), where h is the height in feet. How long will it take for a ball dropped from a height of 64 feet to hit the ground?

• 1 second

• 2 seconds

• 3 seconds

• 4 seconds

A company produces a product that has a profit modeled by the function P(x) = 2√x, where x is the number of units sold. If the company sells 36 units, what is the profit?

• 12

• 10

• 15

• 20

The volume of a cube can be expressed as V(s) = s³, where s is the length of a side. If the volume is 125 cubic inches, what is the length of a side of the cube?

• 3 inches

• 5 inches

• 10 inches

• 7 inches

A cyclist travels a distance modeled by the function d(t) = 4√t, where d is the distance in miles and t is the time in hours. How far does the cyclist travel in 9 hours?

• 12 miles

• 10 miles

• 16 miles

• 8 miles