Exploring Exponential Growth & Decay: Equations & Graphs

A population of 500 rabbits doubles every year. Write an exponential equation to represent the population after 't' years. How many rabbits will there be after 3 years?

• 4000 rabbits

• 5000 rabbits

• 3000 rabbits

• 2000 rabbits

A car's value decreases by 15% each year. If the car is currently worth $20,000, write an exponential decay equation to model its value over time. What will the value be after 4 years?

• $15,000.00

• $10,440.12

• $8,500.00

• $12,000.00

A bacteria culture starts with 200 bacteria and triples every hour. Create an exponential growth equation for the number of bacteria after 'h' hours. How many bacteria will there be after 2 hours?

• 600

• 1800

• 1200

• 2400

A bank account earns 5% interest compounded annually. If you deposit $1,000, write an exponential growth equation to model the account balance after 't' years. What will the balance be after 5 years?

• 1000.00

• 1500.00

• 1102.50

• 1276.28

A tree grows at a rate of 10% per year. If it is currently 3 meters tall, write an equation to model its height over time. How tall will the tree be after 3 years?

• 3.993 meters

• 5.1 meters

• 4.5 meters

• 2.7 meters

A radioactive substance decays at a rate of 25% per hour. If you start with 80 grams, write an exponential decay equation. How much of the substance will remain after 2 hours?

• 45 grams

• 60 grams

• 20 grams

• 30 grams

A certain species of fish in a lake is decreasing by 20% each year due to overfishing. If there are currently 1,000 fish, write an equation to model the fish population over time. How many fish will be left after 3 years?

• 512 fish

• 800 fish

• 640 fish

• 256 fish

A savings account has an initial deposit of $500 and earns 3% interest compounded annually. Write an exponential growth equation for the account balance. What will the balance be after 10 years?

• 671.95

• 600.00

• 750.00

• 500.00

A certain type of mold grows at a rate of 50% every day. If you start with 10 grams, write an equation to model the growth. How much mold will there be after 4 days?

• 40 grams

• 50.625 grams

• 100 grams

• 25 grams

A tree's height is modeled by the equation h(t) = 2(1.1)^t, where h is the height in meters and t is the time in years. Graph this equation for the first 5 years and describe the growth pattern.

• The height of the tree after 5 years is approximately 2.5 meters.

• The height of the tree after 5 years is approximately 4.0 meters.

• The height of the tree after 5 years is approximately 3.221 meters.

• The height of the tree after 5 years is approximately 5.5 meters.