Exploring Rational Exponents in Real-Life Scenarios

A gardener is planting a new type of flower that grows at a rate represented by the function y = x^(1/2). If the area of the garden is 16 square meters, how many meters of the flower can the gardener plant along one side?

• 2 meters

• 8 meters

• 4 meters

• 6 meters

A car's speed can be modeled by the equation s = t^(2/3), where s is the speed in meters per second and t is the time in seconds. If the car travels for 27 seconds, what is its speed?

• 15 m/s

• 12 m/s

• 6 m/s

• 9 m/s

The volume of a cube can be expressed as V = s^(3/2), where s is the length of a side. If the volume of the cube is 64 cubic meters, what is the length of one side?

• 4

• 32

• 16

• 8

A scientist is studying bacteria growth, which can be modeled by the equation N = t^(3/4), where N is the number of bacteria and t is time in hours. If there are 81 bacteria after a certain time, how long did it take?

• 6561 hours

• 27 hours

• 243 hours

• 729 hours

A rectangular garden has a length that is 4 times its width. If the area of the garden is represented by the equation A = w^(3/2) and the area is 64 square meters, what is the width of the garden?

• 16 meters

• 8 meters

• 4 meters

• 2 meters

A water tank's capacity can be modeled by the equation C = h^(2/3), where C is the capacity in liters and h is the height in meters. If the tank can hold 64 liters, what is the height of the tank?

• 32

• 256

• 512

• 128

A rectangular plot of land has a length that is 9 meters longer than its width. If the area is represented by the equation A = w^(5/3) and the area is 729 square meters, what is the width of the plot?

• 21

• 18

• 15

• 12

A cyclist's distance can be modeled by the equation d = t^(4/5), where d is the distance in kilometers and t is the time in hours. If the cyclist travels for 32 hours, how far do they travel?

• 22.10 kilometers

• 15.50 kilometers

• 18.79 kilometers

• 25.00 kilometers

A box's volume is given by the equation V = s^(4/3), where s is the length of a side. If the volume of the box is 81 cubic meters, what is the length of one side?

• 9

• 27

• 18

• 36

A tree's height can be modeled by the equation h = t^(1/2), where h is the height in meters and t is the age in years. If the tree is 9 meters tall, how old is it?

• 100 years

• 81 years

• 45 years

• 64 years