Real-Life Radical Functions: Modeling & Interpreting Solutions

A gardener is designing a circular flower bed with a radius of r meters. The area of the flower bed can be modeled by the function A(r) = πr². If the area is 50 square meters, what is the radius of the flower bed?

• 5 meters

• √(50/π)

• √(100/π)

• 10 meters

A car's speed can be modeled by the function s(t) = √(t + 4), where s is the speed in meters per second and t is the time in seconds. If the car's speed is 10 m/s, how long has the car been traveling?

• 50 seconds

• 80 seconds

• 96 seconds

• 120 seconds

The height of a ball thrown into the air can be modeled by the function h(t) = -4.9t² + 20t + 5, where h is the height in meters and t is the time in seconds. What is the maximum height reached by the ball?

• 30 meters

• 20 meters

• 25.4 meters

• 15.4 meters

A rectangular garden has a length that is 3 meters longer than its width. The area of the garden is 40 square meters. If w is the width, write a radical function to find the width of the garden.

• 7 meters

• 4 meters

• 5 meters

• 6 meters

The volume of a cube can be modeled by the function V(s) = s³, where V is the volume and s is the length of a side. If the volume of the cube is 64 cubic meters, what is the length of a side of the cube?

• 10 meters

• 2 meters

• 8 meters

• 4 meters

A swimming pool is being filled with water. The volume of water in the pool can be modeled by the function V(t) = 2√t, where V is the volume in cubic meters and t is the time in hours. If the volume of water is 18 cubic meters, how long has the pool been filling?

• 36 hours

• 64 hours

• 100 hours

• 81 hours

The distance d in meters that a car travels can be modeled by the function d(t) = 3√t, where t is the time in hours. If the car has traveled 27 meters, how long has it been traveling?

• 81 hours

• 9 hours

• 27 hours

• 54 hours

A triangular piece of land has a base of b meters and a height of h meters. The area can be modeled by the function A(b, h) = (1/2)bh. If the area is 30 square meters and the height is 5 meters, what is the length of the base?

• 8 meters

• 15 meters

• 12 meters

• 10 meters

The time it takes for a ball to hit the ground can be modeled by the function t(h) = √(h/4.9), where h is the height in meters. If the ball is dropped from a height of 20 meters, how long will it take to hit the ground?

• Approximately 2.02 seconds

• Approximately 4.0 seconds

• Approximately 1.5 seconds

• Approximately 3.5 seconds

A rectangular box has a volume of 1000 cubic centimeters. The length is twice the width, and the height is 5 centimeters. Write a radical function to find the width of the box.

• 5 cm

• 15 cm

• 20 cm

• 10 cm