Exploring Exponential Growth and Decay in Real Life

A bacteria culture doubles in size every 3 hours. If the initial amount is 500 bacteria, write an exponential equation to represent the number of bacteria after t hours. How many bacteria will there be after 12 hours?

• 16000

• 2000

• 4000

• 8000

A car's value decreases by 15% each year. If the car is initially worth $20,000, create an exponential decay equation to model its value over time. What will the car's value be after 5 years?

• $12,500.00

• $10,000.00

• $7,610.51

• $5,000.00

A tree grows at a rate of 10% per year. If the tree is currently 4 feet tall, write an exponential equation to represent its height after t years. How tall will the tree be after 3 years?

• 5.32 feet

• 4.40 feet

• 6.00 feet

• 7.20 feet

A radioactive substance decays at a rate of 25% per hour. If you start with 80 grams, write an exponential decay equation for the amount remaining after t hours. How much will remain after 4 hours?

• 30 grams

• 25.3125 grams

• 15 grams

• 40 grams

A population of fish in a lake decreases by 30% each year due to overfishing. If the initial population is 1,000 fish, create an exponential decay equation. How many fish will be left after 2 years?

• 490 fish

• 350 fish

• 800 fish

• 600 fish

A savings account earns 5% interest compounded annually. If you deposit $1,000, write an exponential equation to model the amount in the account after t years. How much will be in the account after 10 years?

• $1,200.00

• $1,500.00

• $1,628.89

• $2,000.00

A certain type of plant grows exponentially, doubling its height every month. If it starts at 2 inches, write an equation to represent its height after t months. What will its height be after 6 months?

• 128 inches

• 64 inches

• 256 inches

• 32 inches

A smartphone loses 20% of its value each year. If it is originally purchased for $800, create an exponential decay equation to model its value over time. What will the value be after 3 years?

• $512.00

• $409.60

• $640.00

• $720.00

A certain species of fish grows exponentially, increasing its population by 50% every year. If the initial population is 200, write an equation to represent the population after t years. How many fish will there be after 4 years?

• 800

• 950

• 1200

• 1013

A certain medication in the bloodstream decreases by 40% every hour. If the initial dosage is 100 mg, write an exponential decay equation to model the amount remaining after t hours. How much will remain after 3 hours?

• 21.6 mg

• 10 mg

• 50 mg

• 30 mg