Exploring Exponential Growth & Recursive Sequences

A population of bacteria doubles every 3 hours. If the initial population is 500, how many bacteria will there be after 12 hours? Graph the exponential growth function.

• 8000

• 10000

• 4000

• 2000

A car's value depreciates by 15% each year. If the car was purchased for $20,000, what will its value be after 5 years? Use a recursive sequence to model the depreciation.

• 8863.26

• 5000

• 12000

• 15000

A bank offers an interest rate of 5% compounded annually. If you deposit $1,000, how much money will you have after 10 years? Graph the exponential growth of your investment.

• $1,200.00

• $2,000.00

• $1,628.89

• $1,500.50

A certain species of fish in a lake grows according to the recursive formula F(n) = F(n-1) + 2, where F(1) = 5. What is the size of the fish population after 10 generations?

• 20

• 23

• 30

• 15

A tree grows 10% taller each year. If the tree is currently 4 meters tall, how tall will it be after 6 years? Create a graph to represent this growth.

• 5.00 meters

• 8.00 meters

• 9.00 meters

• 7.09 meters

A savings account has a balance of $2,000 and earns 3% interest compounded monthly. How much will be in the account after 2 years? Use a recursive sequence to show the monthly balance.

• $2,050.00

• $2,127.49

• $2,300.00

• $1,800.00

A certain virus spreads exponentially, doubling the number of infected individuals every day. If there are 10 infected individuals today, how many will there be in a week? Graph the exponential growth of the infection.

• 640

• 2560

• 1280

• 5120

A sequence is defined recursively as S(n) = 3S(n-1) - 2 with S(1) = 1. Find the 5th term of the sequence and explain the pattern you observe.

• 5

• 1

• 2

• 4

A population of rabbits increases according to the recursive formula P(n) = P(n-1) + 5, starting with P(1) = 10. How many rabbits will there be after 15 months?

• 100

• 90

• 80

• 75