Linear vs. Exponential Functions: Graphing Challenges

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) based on the number of miles (m) driven. Graph this equation.

• C = 50 + 0.20m

• C = 50 + 0.50m

• C = 50 - 0.20m

• C = 0.20m - 50

A population of bacteria doubles every hour. If you start with 100 bacteria, write an exponential function to represent the population after t hours. How many bacteria will there be after 5 hours?

• 4000

• 3200

• 1600

• 800

A gym membership costs $30 to join and $25 per month. Create a linear equation for the total cost (C) after m months. How would you graph this equation?

• C = 25m

• C = 30 + 25m

• C = 30m + 25

• C = 30 + 30m

A tree grows at a rate of 3 inches per year. If it is currently 5 feet tall, write a linear function to represent its height (h) after y years. How would you graph this function?

• h(y) = 60 + 3y

• h(y) = 60 - 3y

• h(y) = 36 + 3y

• h(y) = 5 + 3y

A savings account has an initial deposit of $1,000 and earns 5% interest compounded annually. Write an exponential function to represent the amount (A) in the account after t years. How would you graph this function?

• A(t) = 1000 + 0.05t

• A(t) = 1000(1.05)t

• A(t) = 1000(1.05)^t

• A(t) = 1000(0.95)^t

A taxi charges a base fare of $3 plus $2 for each mile traveled. Write a linear equation for the total fare (F) based on the number of miles (m) traveled. How would you graph this equation?

• F = 2m + 3

• F = 3 + 2m

• F = 3m + 2

• F = 5 + 2m

A certain species of fish in a lake is known to increase its population by 10% each year. If the current population is 200 fish, write an exponential function to represent the population after t years. How many fish will there be after 3 years?

• 220 fish

• 250 fish

• 300 fish

• 266 fish

A plant grows exponentially, doubling its height every week. If it starts at 2 inches, write an exponential function to represent its height (h) after w weeks. How tall will it be after 4 weeks?

• 64 inches

• 32 inches

• 16 inches

• 8 inches

A delivery service charges a flat fee of $15 plus $1.50 per mile. Write a linear equation for the total cost (C) based on the distance (d) in miles. How would you graph this equation?

• C = 1.5d + 10

• C = 15 + 2d

• C = 15 - 1.5d

• C = 15 + 1.5d