Growth Rates Showdown: Linear vs Exponential Challenges

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 with a rental company that charges $10 for the first day and $5 for each additional day. Which is cheaper?

• Both rental companies cost the same at $50.

• The first rental company is cheaper at $150.

• The second rental company is cheaper at $30.

• The second rental company costs $40.

A population of rabbits doubles every month. If there are initially 10 rabbits, how many will there be after 6 months? Compare this with a linear growth of 10 rabbits added each month. Which growth is faster?

• 300 rabbits after 6 months.

• 640 rabbits after 6 months.

• 50 rabbits after 6 months.

• 120 rabbits after 6 months.

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 start with $200, how much will you have in 10 years at each bank?

• Savings account: $600, Compound interest account: $700

• Savings account: $700, Compound interest account: $800

• Savings account: $800, Compound interest account: $900

• Savings account: $500, Compound interest account: $600

A gardener plants 100 seeds, and each week, he plants an additional 20 seeds. How many seeds will he have planted after 8 weeks? Compare this with a scenario where the seeds double each week. How many seeds will he have after 8 weeks in that case?

• After 8 weeks, the gardener will have planted 300 seeds in the first scenario and 12800 seeds in the doubling scenario.

• After 8 weeks, the gardener will have planted 260 seeds in the first scenario and 25600 seeds in the doubling scenario.

• After 8 weeks, the gardener will have planted 200 seeds in the first scenario and 51200 seeds in the doubling scenario.

• After 8 weeks, the gardener will have planted 240 seeds in the first scenario and 10240 seeds in the doubling scenario.

A smartphone app has 1,000 users and gains 100 new users each month. How many users will it have after 12 months? Compare this with an app that starts with 1,000 users and doubles its users every 3 months. Which app has more users after 12 months?

• The second app has more users after 12 months.

• The first app has more users after 12 months.

• The first app has 1,200 users after 12 months.

• Both apps have the same number of users after 12 months.

A factory produces 200 toys per day. If production increases by 50 toys each day, how many toys will be produced in 10 days? Compare this with a factory that starts with 200 toys and doubles its production every 5 days. Which factory produces more toys in 10 days?

• The first factory produces 3500 toys, while the second factory produces 2500 toys.

• The first factory produces 4000 toys, while the second factory produces 3000 toys.

• The first factory produces 5000 toys, while the second factory produces 2000 toys.

• The first factory produces 3000 toys, while the second factory produces 4000 toys.

A town's population is 5,000 and grows by 200 people each year. After 10 years, what will the population be? Compare this with a town that has a population of 5,000 and doubles every 10 years. Which town has a larger population after 10 years?

• The first town has a larger population after 10 years.

• The first town's population is 6,000 after 10 years.

• The second town has a larger population after 10 years.

• Both towns have the same population after 10 years.

A subscription service charges $15 per month. If you subscribe for a year, how much will you pay? Compare this with a service that starts at $5 and doubles its price every 6 months. How much will you pay after a year?

• $200 for the first service and $30 for the second service

• The first service costs $180, while the second service costs $35.

• $150 for the first service and $40 for the second service

• $120 for the first service and $60 for the second service

A tree grows 3 inches every year. If it is currently 4 feet tall, how tall will it be in 10 years? Compare this with a tree that grows exponentially, doubling its height every 5 years. How tall will that tree be in 10 years?

• 7 feet tall for the first tree and 20 feet tall for the second tree.

• 4 feet tall for the first tree and 8 feet tall for the second tree.

• 5 feet tall for the first tree and 10 feet tall for the second tree.

• The first tree will be 6.5 feet tall, and the second tree will be 16 feet tall.

A video game has 500 players and gains 50 new players each week. How many players will it have after 20 weeks? Compare this with a game that starts with 500 players and doubles its player base every 4 weeks. Which game has more players after 20 weeks?

• Both games have the same number of players after 20 weeks.

• The second game has more players after 20 weeks.

• The first game has more players after 20 weeks.

• The first game will have 1,000 players after 20 weeks.