Real-World Applications of Geometric Sequences in Action

A bacteria culture doubles in size every hour. If the initial size is 500 bacteria, write an explicit formula for the number of bacteria after t hours. How many bacteria will there be after 5 hours?

• 8000

• 16000

• 20000

• 4000

A car's value decreases by 20% each year. If the car's initial value is $20,000, write an explicit formula for its value after t years. What will the value be after 3 years?

• $12,000

• $8,000

• $15,360

• $10,240

A tree grows 1.5 times its height every year. If the tree is initially 2 meters tall, write an explicit formula for its height after t years. How tall will the tree be after 4 years?

• 6.0 meters

• 8.5 meters

• 12.75 meters

• 10.125 meters

A savings account earns interest at a rate of 5% compounded annually. If you start with $1,000, write an explicit formula for the amount in the account after t years. How much will be in the account after 6 years?

• 1200.00

• 1340.10

• 1000.00

• 1500.00

A video game character earns 150 points for each level completed, and the points earned double every 3 levels. Write an explicit formula for the points earned after n levels. How many points will the character have after completing 9 levels?

• 1800

• 900

• 1200

• 1500

A population of fish in a lake is increasing geometrically. If there are initially 200 fish and the population triples every year, write an explicit formula for the population after t years. What will the population be after 2 years?

• 2400

• 1800

• 600

• 1200

A cell phone plan offers 1 GB of data for the first month, and the data allowance doubles each subsequent month. Write an explicit formula for the data allowance after t months. How much data will be available after 5 months?

• 8 GB

• 16 GB

• 4 GB

• 32 GB

A company produces 100 units of a product in the first month, and production doubles every month. Write an explicit formula for the number of units produced after t months. How many units will be produced in the 6th month?

• 4000

• 3200

• 2400

• 1600

A tree's height is 3 feet and it grows by a factor of 1.2 each year. Write an explicit formula for the height of the tree after t years. What will the height be after 5 years?

• 5.5 feet

• 8.2 feet

• 7.46496 feet

• 10 feet

A loan of $5,000 has an interest rate of 10% compounded annually. Write an explicit formula for the amount owed after t years. How much will be owed after 4 years?

• 8000.00

• 6000.00

• 5000.00

• 7320.50