7th Grade Challenge: Identify Linear & Exponential Functions

1. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write a table showing the total cost for driving 0, 50, 100, and 150 miles. Is this a linear or exponential function?

• 0 miles - $30, 50 miles - $45, 100 miles - $70, 150 miles - $90. This is a linear function.

• 0 miles - $30, 50 miles - $35, 100 miles - $45, 150 miles - $55. This is a quadratic function.

• 0 miles - $20, 50 miles - $30, 100 miles - $40, 150 miles - $50. This is an exponential function.

• The total costs are: 0 miles - $30, 50 miles - $40, 100 miles - $50, 150 miles - $60. This is a linear function.

2. A bacteria culture doubles in size every hour. If you start with 5 bacteria, create a table showing the number of bacteria after 0, 1, 2, and 3 hours. Is this a linear or exponential function?

• Exponential function

• Quadratic function

• Constant function

• Linear function

3. A gym membership costs $25 per month. Create a table showing the total cost for 1, 3, 6, and 12 months. Identify if this is linear or exponential.

• Total cost for 1 month: $30, 3 months: $90, 6 months: $180, 12 months: $360. This is an exponential relationship.

• Total cost for 1 month: $20, 3 months: $60, 6 months: $120, 12 months: $240. This is a linear relationship.

• Total cost for 1 month: $25, 3 months: $75, 6 months: $150, 12 months: $300. This is a linear relationship.

• Total cost for 1 month: $25, 3 months: $80, 6 months: $150, 12 months: $300. This is a linear relationship.

4. A tree grows 3 inches every year. If it is currently 5 feet tall, create a table showing its height after 1, 2, 3, and 4 years. Is this a linear or exponential function?

• The height of the tree after 1 year is 58 inches, after 2 years is 61 inches, after 3 years is 64 inches, and after 4 years is 67 inches. This is a linear function.

• The height of the tree after 1 year is 60 inches, after 2 years is 65 inches, after 3 years is 70 inches, and after 4 years is 75 inches. This is an exponential function.

• The height of the tree after 1 year is 63 inches, after 2 years is 66 inches, after 3 years is 69 inches, and after 4 years is 72 inches. This is a linear function.

• The height of the tree after 1 year is 70 inches, after 2 years is 75 inches, after 3 years is 80 inches, and after 4 years is 85 inches. This is a quadratic function.

5. A savings account earns 5% interest compounded annually. If you start with $100, create a table showing the balance after 1, 2, and 3 years. Is this linear or exponential growth?

• Balances after 1, 2, and 3 years are 105, 110.25, and 115.76 respectively. This is exponential growth.

• Balances after 1, 2, and 3 years are 105, 112.5, and 120 respectively. This is linear growth.

• Balances after 1, 2, and 3 years are 105, 110, and 115 respectively. This is linear growth.

• Balances after 1, 2, and 3 years are 105, 110.25, and 120.5 respectively. This is exponential growth.

6. A phone plan offers unlimited data for $50 a month. Write a table showing the total cost for 1, 2, 3, and 4 months. Is this a linear or exponential function?

• The total cost for 1 month is $30, for 2 months is $60, for 3 months is $90, and for 4 months is $120. This is a quadratic function.

• The total cost for 1 month is $50, for 2 months is $150, for 3 months is $250, and for 4 months is $350. This is an exponential function.

• The total cost for 1 month is $50, for 2 months is $100, for 3 months is $150, and for 4 months is $200. This is a linear function.

• The total cost for 1 month is $50, for 2 months is $100, for 3 months is $200, and for 4 months is $300. This is a linear function.

7. A population of fish in a lake increases by 10% each year. If there are currently 200 fish, create a table showing the population after 1, 2, and 3 years. Is this linear or exponential growth?

• Exponential growth

• Linear growth

• Decreasing growth

• Constant growth

8. A factory produces 100 widgets in the first hour and increases production by 50 widgets each hour. Create a table showing production for the first 4 hours. Is this a linear or exponential function?

• Cubic function

• Quadratic function

• Linear function

• Constant function

9. A plant grows 2 inches the first week and then grows 2 inches more each subsequent week. Create a table showing its height after 1, 2, 3, and 4 weeks. Is this linear or exponential growth?

• Exponential growth

• No growth

• Linear growth

• Variable growth

10. A loan of $1,000 has an interest rate of 10% compounded annually. Create a table showing the amount owed after 1, 2, and 3 years. Is this linear or exponential?

• The amounts owed after 1, 2, and 3 years are $1100, $1210, and $1331 respectively. This is exponential growth.

• $1200, $1400, $1600 respectively. This is linear growth.

• $1000, $2000, $3000 respectively. This is exponential growth.

• $1050, $1100, $1150 respectively. This is linear growth.