Exponential vs Linear Growth: Word Problems Challenge

A car rental company charges a flat fee of $30 per day. If you rent a car for 5 days, how much will it cost? Compare this to a rental company that charges $10 for the first day and doubles the price each subsequent day. How much would it cost to rent the car for 5 days at the second company?

• $200 and $400

• $150 and $250

• $100 and $200

• The first company costs $150 and the second company costs $310.

A population of bacteria doubles every hour. If you start with 100 bacteria, how many will there be after 5 hours? Compare this to a linear growth model where the population increases by 50 bacteria each hour. How many bacteria will there be after 5 hours in that case?

• 1500 bacteria after 5 hours for exponential growth; 250 bacteria after 5 hours for linear growth.

• 2000 bacteria after 5 hours for exponential growth; 400 bacteria after 5 hours for linear growth.

• 500 bacteria after 5 hours for exponential growth; 300 bacteria after 5 hours for linear growth.

• 3200 bacteria after 5 hours for exponential growth; 350 bacteria after 5 hours for linear growth.

A bank offers a savings account with a linear interest rate of $50 per year. Another bank offers compound interest that doubles your money every 5 years. If you deposit $1,000, how much will you have in 10 years at each bank?

• $1,500 at the first bank and $4,000 at the second bank.

• $1,200 at the first bank and $3,000 at the second bank.

• $1,000 at the first bank and $5,000 at the second bank.

• $1,800 at the first bank and $2,500 at the second bank.

A tree grows 2 feet every year (linear growth). Another tree grows exponentially, doubling its height every year. If the first tree is 3 feet tall, how tall will each tree be after 4 years?

• Tree 1: 9 feet, Tree 2: 24 feet

• Tree 1: 10 feet, Tree 2: 32 feet

• Tree 1: 12 feet, Tree 2: 64 feet

• Tree 1: 11 feet, Tree 2: 48 feet

A subscription service charges $15 per month (linear) while another service offers a free trial for the first month and then charges $10 per month thereafter (exponential growth in cost). How much will you pay after 6 months for each service?

• First service: $70, Second service: $70

• First service: $90, Second service: $50

• First service: $80, Second service: $60

• First service: $100, Second service: $40

A town's population is currently 10,000 and is expected to grow by 1,000 people each year (linear). Another town's population is 5,000 and is expected to double every 3 years (exponential). How many people will be in each town after 6 years?

• Town 1: 15000, Town 2: 10000

• Town 1: 12000, Town 2: 25000

• Town 1: 18000, Town 2: 15000

• Town 1: 16000, Town 2: 20000

A cell phone plan costs $40 per month plus $0.10 per text message (linear). Another plan costs $20 for the first month and then increases by $5 each month (exponential). How much will you pay for 6 months with each plan if you send 100 texts each month?

• Plan 1: $320, Plan 2: $210

• Plan 1: $250, Plan 2: $180

• Plan 1: $300, Plan 2: $150

• Plan 1: $300, Plan 2: $195

A factory produces 200 toys per day (linear). If the production doubles every week (exponential), how many toys will be produced in 4 weeks?

• 8000

• 6400

• 4000

• 11200

A video game character earns 100 points for each level completed (linear). If the points earned double for each level after the first (exponential), how many points will the character have after completing 5 levels?

• 3100

• 5000

• 2100

• 1500

A farmer plants 100 seeds that grow linearly at a rate of 10 seeds per week. Another farmer plants 50 seeds that double every week. How many seeds will each farmer have after 4 weeks?

• Farmer 1: 120 seeds, Farmer 2: 600 seeds

• Farmer 1: 140 seeds, Farmer 2: 800 seeds

• Farmer 1: 160 seeds, Farmer 2: 1000 seeds

• Farmer 1: 100 seeds, Farmer 2: 400 seeds