Real-Life Applications of Rational Exponents for 9th Graders

A gardener is planting a new type of flower that grows at a rate represented by the equation h = 4^(1/2)t, where h is the height in inches and t is the time in weeks. How tall will the flowers be after 9 weeks?

• 12 inches

• 30 inches

• 24 inches

• 18 inches

A car's value decreases according to the equation V = 20,000(1/2)^(t/5), where V is the value in dollars and t is the time in years. What will the value of the car be after 10 years?

• 5000

• 15000

• 2500

• 10000

A scientist is studying bacteria growth, which can be modeled by the equation N = 100(3/4)^(t/2), where N is the number of bacteria and t is the time in hours. How many bacteria will there be after 6 hours?

• 75

• 30

• 42

• 50

A rectangular garden has an area of 64 square feet. If the length is represented by the equation L = 4^(1/2)x, where x is the width in feet, what is the width of the garden?

• 4 feet

• 8 feet

• 10 feet

• 6 feet

A student is saving money for college. The amount saved can be modeled by the equation A = 500(1.05)^(t/12), where A is the amount in dollars and t is the time in months. How much will the student have saved after 3 years?

• $700.25

• $600.50

• $578.81

• $450.00

A water tank is filled at a rate described by the equation V = 200(1/3)^(t/4), where V is the volume in liters and t is the time in hours. What will the volume of water be after 8 hours?

• 50 liters

• 22.22 liters

• 10 liters

• 5 liters

A tree grows according to the equation h = 10(2)^(t/3), where h is the height in feet and t is the time in years. How tall will the tree be after 9 years?

• 80 feet

• 100 feet

• 60 feet

• 40 feet

A population of fish in a lake can be modeled by the equation P = 500(0.9)^(t/2), where P is the population and t is the time in years. What will the population be after 6 years?

• 365

• 600

• 250

• 450

A cyclist travels a distance represented by the equation d = 16(1/2)^(t/3), where d is the distance in miles and t is the time in hours. How far will the cyclist travel after 9 hours?

• 1 mile

• 2 miles

• 4 miles

• 8 miles

A company’s profit can be modeled by the equation P = 1000(1.1)^(t/5), where P is the profit in dollars and t is the time in years. What will the profit be after 10 years?

• 2000

• 1500

• 1210

• 1000