Linear vs Exponential: Fun Function Challenges for 8th Grade

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. What is the cost for driving 100 miles?

• $50

• $100

• $70

• $90

A bacteria culture doubles in size every hour. If the initial size is 500 bacteria, write an exponential function to represent the size of the culture after t hours. How many bacteria will there be after 4 hours?

• 16000

• 8000

• 4000

• 1000

A gym membership costs $30 per month with a one-time registration fee of $50. Create a linear equation to represent the total cost (C) after m months. What is the total cost after 6 months?

• $180

• $150

• $200

• $230

A population of rabbits grows exponentially. If there are initially 10 rabbits and the population triples every month, write an exponential function to represent the population after t months. How many rabbits will there be after 3 months?

• 90

• 150

• 360

• 270

A phone plan charges a base fee of $25 and an additional $10 for each gigabyte of data used. Write a linear equation for the total cost (C) based on the number of gigabytes (g) used. What is the cost for using 5 gigabytes?

• $50

• $60

• $75

• $100

A tree grows 2 inches every year. Write a linear function to represent the height (h) of the tree after y years if it starts at 5 inches. What will be the height after 10 years?

• 30 inches

• 25 inches

• 15 inches

• 20 inches

A savings account has an initial deposit of $1000 and earns 5% interest compounded annually. Write an exponential function to represent the amount (A) in the account after t years. How much will be in the account after 3 years?

• 1300.75

• 1157.63

• 1100.50

• 1200.00

A factory produces 200 units of a product in the first week and increases production by 50 units each subsequent week. Write a linear equation to represent the total production (P) after w weeks. How many units will be produced after 5 weeks?

• 300 units

• 400 units

• 450 units

• 350 units

A certain species of fish in a lake is known to double in population every year. If there are currently 200 fish, write an exponential function to represent the population after y years. How many fish will there be after 5 years?

• 6400

• 4000

• 12800

• 3200

A subscription service charges $15 per month. If you sign up for a year, you get a 10% discount on the total cost. Write a linear equation for the total cost (C) for m months. What is the total cost for 12 months with the discount applied?

• 162

• 180

• 150

• 120