Linear vs. Exponential Functions: Graphing Challenge

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a linear function to represent the total cost (C) based on the number of miles driven (m). Graph this function for 0 to 100 miles.

• C = 30m + 0.20

• C = 30 + 0.20m

• C = 10 + 0.30m

• C = 30 + 0.50m

A population of bacteria doubles every hour. If you start with 100 bacteria, write an exponential function to represent the population (P) after t hours. Graph this function for t from 0 to 5 hours.

• P(t) = 50 * 2^t

• P(t) = 100 * 2^t

• P(t) = 100 + 2^t

• P(t) = 100 * 3^t

A gym membership costs $50 to join and $25 per month. Write a linear function to represent the total cost (C) after m months. How much will it cost after 6 months?

• 100

• 250

• 150

• 200

A tree grows 3 inches every year. If it is currently 5 feet tall, write a linear function to represent its height (H) after y years. Graph this function for y from 0 to 10 years.

• H(y) = 60 + 3y

• H(y) = 36 + 3y

• H(y) = 15 + 3y

• H(y) = 5 + 3y

A savings account has an initial deposit of $200 and earns 5% interest compounded annually. Write an exponential function to represent the amount (A) in the account after t years. Graph this function for t from 0 to 10 years.

• A(t) = 200(1.10)^t

• A(t) = 200(0.95)^t

• A(t) = 200 + 0.05t

• A(t) = 200(1.05)^t

A taxi charges a base fare of $2.50 and $1.50 for each mile traveled. Write a linear function to represent the total fare (F) based on the number of miles (m). How much would a 10-mile trip cost?

• $20.00

• $17.50

• $15.00

• $12.50

A certain species of fish in a lake is estimated to grow exponentially. If the current population is 500 and it increases by 10% each year, write an exponential function to represent the population (P) after t years. Graph this function for t from 0 to 5 years.

• P(t) = 500 + 50t

• P(t) = 500 * (1.05)^t

• P(t) = 500 * (1.10)^t

• P(t) = 500 * (2)^t

A phone plan costs $40 per month plus $0.10 per text message sent. Write a linear function to represent the total cost (C) based on the number of text messages (t). How much will it cost if you send 200 texts?

• $80

• $60

• $100

• $40

A plant grows at a rate of 2 inches per week. If it starts at 10 inches tall, write a linear function to represent its height (H) after w weeks. Graph this function for w from 0 to 8 weeks.

• H(w) = 2w + 5

• H(w) = 10 + w

• H(w) = 10 - 2w

• H(w) = 10 + 2w

A city’s population is currently 1,000 and is expected to grow exponentially at a rate of 3% per year. Write an exponential function to represent the population (P) after t years. Graph this function for t from 0 to 10 years.

• P(t) = 1000 * e^(0.03t)

• P(t) = 1000 * (1 + 0.03)^t

• P(t) = 1000 * e^(0.03t^2)

• P(t) = 1000 * 0.03^t