Rational Exponents in Real-World Word Problems

A gardener is planting a tree that grows at a rate of 1/2 of its height each year. If the tree is currently 16 feet tall, how tall will it be after 3 years? Solve for the height using rational exponents.

• 48 feet

• 32 feet

• 40 feet

• 54 feet

A car's value decreases by 20% each year. If the car is currently worth $25,000, what will its value be after 2 years? Use a rational exponent to find the answer.

• $20,000

• $16,000

• $22,000

• $18,000

A rectangular garden has a length that is 4 times its width. If the area of the garden is 64 square feet, what is the width of the garden? Solve the equation using rational exponents.

• 4 feet

• 2 feet

• 8 feet

• 16 feet

A scientist is studying bacteria that double in number every hour. If there are currently 100 bacteria, how many will there be after 5 hours? Use rational exponents to solve the problem.

• 2000

• 1500

• 4000

• 3200

A cube has a volume of 729 cubic inches. What is the length of one side of the cube? Use rational exponents to find the side length.

• 9 inches

• 6 inches

• 12 inches

• 15 inches

A student is saving money for a new laptop. If she saves $200 and her savings grow at a rate of 5% per year, how much will she have after 3 years? Use a rational exponent to calculate her total savings.

• 200.00

• 250.00

• 210.00

• 231.53

A water tank is filled to 1/4 of its capacity. If the tank can hold 1000 liters, how many liters of water are currently in the tank? Solve using rational expressions.

• 500 liters

• 250 liters

• 750 liters

• 100 liters

A rectangular pool has a length that is 3 times its width. If the perimeter of the pool is 48 meters, what is the width of the pool? Use rational exponents to solve the equation.

• 4 meters

• 6 meters

• 10 meters

• 8 meters

A recipe calls for 2 cups of flour, but you want to make only 1/4 of the recipe. How much flour do you need? Use rational expressions to find the answer.

• 1/2 cup

• 1/4 cup

• 3/4 cup

• 1 cup

A box has a volume of 512 cubic centimeters. If the box is a cube, what is the length of one side? Solve using rational exponents to find the side length.

• 6 centimeters

• 8 centimeters

• 12 centimeters

• 10 centimeters