Exploring Linear vs Exponential Growth: Tables & Comparisons

1. A plant grows 2 inches every week (linear growth). Create a table showing its height over 5 weeks. How does this compare to a plant that doubles its height every week (exponential growth)?

• Linear growth: [2, 4, 6, 8, 10]; Exponential growth: [1, 2, 4, 8, 16]

• Linear growth: [0, 2, 4, 6, 8]; Exponential growth: [1, 3, 9, 27, 81]

• Linear growth: [2, 5, 8, 11, 14]; Exponential growth: [2, 4, 8, 16, 32]

• Linear growth: [1, 3, 5, 7, 9]; Exponential growth: [1, 3, 6, 12, 24]

2. A car travels at a constant speed of 60 miles per hour (linear). Create a table showing the distance traveled over 5 hours. How does this compare to a car that starts at 1 mile and doubles its distance every hour (exponential)?

• The car at constant speed travels 200 miles, while the doubling distance car travels 64 miles.

• The car at constant speed travels 300 miles, while the doubling distance car travels 8 miles.

• The car at constant speed travels 300 miles, while the doubling distance car travels 16 miles.

• The car at constant speed travels 250 miles, while the doubling distance car travels 32 miles.

3. A bank offers a savings account with a fixed interest rate of 5% per year (linear). Create a table showing the total amount saved after 5 years. Compare this to an account that compounds interest at 5% annually (exponential).

• Linear: $1200, Compound: $1300

• Linear: $1250, Compound: $1276.28

• Linear: $1500, Compound: $1400

• Linear: $1000, Compound: $1100

4. A video game character earns 100 points every level (linear). Create a table showing total points after 5 levels. How does this compare to a character that earns double the points of the previous level (exponential)?

• Linear: 400 points, Exponential: 1500 points

• Linear: 500 points, Exponential: 3100 points

• Linear: 600 points, Exponential: 2500 points

• Linear: 500 points, Exponential: 2000 points

5. A subscription service charges $10 per month (linear). Create a table showing total cost over 6 months. Compare this to a service that starts at $1 and doubles the price each month (exponential).

• Linear service total cost over 6 months: $60; Exponential service total cost over 6 months: $63.

• Linear service total cost over 6 months: $60; Exponential service total cost over 6 months: $50.

• Linear service total cost over 6 months: $80; Exponential service total cost over 6 months: $60.

• Linear service total cost over 6 months: $50; Exponential service total cost over 6 months: $70.

6. A bacteria culture grows by 50 bacteria every hour (linear). Create a table for 5 hours. How does this compare to a culture that doubles in size every hour (exponential)?

• Linear growth results in 150 bacteria, while exponential growth results in 128 bacteria after 5 hours.

• Linear growth results in 250 bacteria, while exponential growth results in 32 bacteria after 5 hours.

• Linear growth results in 300 bacteria, while exponential growth results in 64 bacteria after 5 hours.

• Linear growth results in 200 bacteria, while exponential growth results in 16 bacteria after 5 hours.

7. A tree grows 3 feet every year (linear). Create a table showing its height over 4 years. Compare this to a tree that grows 3 times its height every year (exponential).

• Linear growth heights: [0, 3, 6, 9, 10]; Exponential growth heights: [1, 2, 4, 8, 16].

• Linear growth heights: [0, 3, 6, 12, 15]; Exponential growth heights: [1, 3, 6, 12, 24].

• Linear growth heights: [0, 3, 6, 9, 12]; Exponential growth heights: [1, 3, 9, 27, 81].

• Linear growth heights: [0, 3, 6, 9, 15]; Exponential growth heights: [1, 2, 4, 8, 16].

8. A factory produces 200 toys each day (linear). Create a table for production over 5 days. How does this compare to a factory that doubles its production every day (exponential)?

• Linear production: 600 toys over 5 days; Exponential production: 1600 toys over 5 days.

• Linear production: 1200 toys over 5 days; Exponential production: 4000 toys over 5 days.

• Linear production: 800 toys over 5 days; Exponential production: 2400 toys over 5 days.

• Linear production: 1000 toys over 5 days; Exponential production: 3200 toys over 5 days.

9. A savings account earns $50 every month (linear). Create a table for 6 months. Compare this to an account that starts with $10 and doubles the amount earned each month (exponential).

• Linear account total: $350, Exponential account total: $400

• Linear account total: $250, Exponential account total: $300

• Linear account total: $300, Exponential account total: $300

• Linear account total: $300, Exponential account total: $320

10. A fitness app tracks calories burned at a steady rate of 200 calories per day (linear). Create a table for 7 days. How does this compare to an app that doubles the calories burned each day (exponential)?

• Linear app: 1400 calories over 7 days; Exponential app: 12800 calories over 7 days.

• Linear app: 1200 calories over 7 days; Exponential app: 12800 calories over 7 days.

• Linear app: 1000 calories over 7 days; Exponential app: 51200 calories over 7 days.

• Linear app: 1400 calories over 7 days; Exponential app: 25600 calories over 7 days.