Real-World Applications of Exponential Models in Growth

A car's value depreciates by 15% each year. If the car is worth $20,000 now, write an exponential decay function to represent its value over time. How much will the car be worth after 5 years?

• $12,000.00

• $5,000.00

• $8,874.37

• $15,000.00

A bank offers an account that compounds interest annually at a rate of 5%. If you deposit $1,000, write an exponential function to model the account balance over time. Graph the function for 10 years.

• A(t) = 1000(1.05)t

• A(t) = 1000(1.05)^t

• A(t) = 1000(0.05)^t

• A(t) = 1000 + 1000(0.05)^t

A certain species of fish in a lake is increasing exponentially. If the current population is 500 and it grows by 20% each year, write an exponential growth function. How many fish will there be in 5 years?

• 1000

• 1500

• 1244

• 600

A researcher finds that a certain virus spreads exponentially. If there are 50 infected individuals and the number of infections doubles every week, write a function to model this. How many infections will there be after 4 weeks?

• 400

• 1000

• 200

• 800

A tree grows at a rate of 10% per year. If its current height is 2 meters, write an exponential growth function to model its height over time. Graph this function for 10 years.

• H(t) = 2 * (2)^t

• H(t) = 2 + 0.10t

• H(t) = 2 * (1.10)^t

• H(t) = 2 * (0.90)^t

A city’s population is currently 1 million and is expected to grow at a rate of 3% per year. Write an exponential growth model for the population and determine the population after 15 years.

• Approximately 1,800,000

• Approximately 1,200,000

• Approximately 1,400,000

• Approximately 1,570,800

A certain investment grows exponentially at a rate of 8% per year. If you invest $5,000, write the exponential function for the investment's growth. How much will it be worth in 10 years?

• $8,000.00

• $9,300.20

• $10,794.50

• $12,500.75

A smartphone app downloads increase exponentially. If there are currently 1,000 downloads and the downloads double every month, write a function to model this growth. How many downloads will there be in 6 months?

• 32000

• 50000

• 64000

• 128000

A scientist is studying a radioactive substance that decays exponentially. If the initial amount is 80 grams and it decays by 25% each year, write the exponential decay function and determine how much will remain after 3 years.

• 20 grams

• 40 grams

• 50 grams

• 33.75 grams