Graphing Linear & Exponential Functions for 8th Graders

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 bacteria culture doubles in size every hour. If the initial size is 100 bacteria, write an exponential equation to represent the size (S) after t hours. Graph this equation for the first 5 hours.

• S = 100 * 3^t

• S = 100 + 2t

• S = 100 * 2^(t+1)

• S = 100 * 2^t, sizes after 5 hours: [100, 200, 400, 800, 1600, 3200]

A gym membership costs $30 per month. If you also pay a one-time registration fee of $50, write a linear equation for the total cost (C) after m months. How would you graph this equation?

• C = 30m - 50

• C = 50m + 30

• C = 30 + 50m

• C = 30m + 50

A population of rabbits grows exponentially. If there are initially 50 rabbits and the population triples every year, write an exponential equation for the population (P) after y years. Graph this equation for the first 4 years.

• P = 50 * 3^y

• P = 50 * y^3

• P = 50 + 3y

• P = 50 * 2^y

A phone plan costs $40 per month plus $0.10 per text message. Write a linear equation for the total cost (C) based on the number of text messages (t) sent. How would you graph this equation?

• C = 40 + 0.10t

• C = 0.10t - 40

• C = 0.10 + 40t

• C = 40t + 0.10

A tree grows 5 inches every year. Write a linear equation to represent the height (H) of the tree after y years if it starts at 3 feet. Graph this equation for the first 10 years.

• H = 60 + 5y

• H = 5y

• H = 3 + 5y

• H = 36 + 5y

A savings account earns 5% interest compounded annually. If you start with $1,000, write an exponential equation for the amount (A) after t years. Graph this equation for the first 5 years.

• A = 1000(1.05)^t

• A = 1000(1.10)^t

• A = 1000(0.95)^t

• A = 1000(1.05)^(t+1)

A factory produces 200 units of a product in the first month and increases production by 50 units each subsequent month. Write a linear equation for the total production (P) after m months. How would you graph this equation?

• P = 200m + 50

• P = 150m + 50

• P = 50m + 200

• P = 50m + 150

A certain species of fish in a lake grows exponentially. If there are 200 fish and the population doubles every 3 months, write an exponential equation for the fish population (F) after t months. Graph this equation for the first year.

• F(t) = 200 + 2t

• F(t) = 200 * 2^(t/3)

• F(t) = 200 * 2^(t/6)

• F(t) = 200 * 3^(t/3)

A subscription service charges $15 per month. If you want to find the total cost (C) after m months, write a linear equation. How would you graph this equation?

• C = 15 + m

• C = 15m

• C = 10m

• C = 15m + 5