Exploring Exponential Functions: Solve & Determine Ranges

1. A population of bacteria doubles every 3 hours. If the initial population is 100, what will be the population after 12 hours? Determine the range of the function representing the population over time.

• 400

• 1600

• 800

• 3200

2. A car's value decreases exponentially over time. If the car is worth $20,000 now and loses 15% of its value each year, what will its value be after 5 years? What is the range of values the car can take over time?

• $5,000 after 5 years; range of values: (0, 5000]

• Approximately $8,874.34 after 5 years; range of values: (0, 20000].

• $12,000 after 5 years; range of values: (0, 12000]

• $15,000 after 5 years; range of values: (0, 15000]

3. The height of a plant grows exponentially. If it starts at 2 cm and grows at a rate of 50% per week, how tall will it be after 4 weeks? What is the range of possible heights after this time?

• 8.5 cm

• 15.75 cm

• 10.125 cm

• 12.0 cm

4. A bank account earns interest exponentially. If you deposit $1,000 at an annual interest rate of 5%, how much will you have after 10 years? Determine the range of the account balance over this period.

• $1,628.89

• $1,200.00

• $2,000.00

• $1,500.50

6. A certain species of fish in a lake grows exponentially. If the initial population is 500 and it increases by 20% each year, what will the population be after 3 years? What is the range of the population over this time?

• 600

• 864

• 1000

• 720

7. A smartphone's battery life decreases exponentially. If it starts with a full charge of 100% and loses 10% of its charge every hour, how much charge will be left after 5 hours? Determine the range of battery life over this period.

• Approximately 59.05%

• 45%

• 70%

• 80%

8. The value of a house increases exponentially. If a house is worth $300,000 now and appreciates at a rate of 4% per year, what will its value be in 10 years? What is the range of possible values for the house?

• $444072

• $400,000

• $500,000

• $350,000

9. A savings account compounds interest exponentially. If you invest $2,000 at an interest rate of 3% compounded annually, how much will you have after 8 years? Determine the range of the account balance over this time.

• $2,200.00

• $3,000.00

• $2,533.54

• $2,000.00

10. A tree grows exponentially, starting at 1 meter and increasing by 30% each year. How tall will the tree be after 5 years? What is the range of heights the tree can achieve over this period?

• The tree will be 2.5 meters tall after 5 years, with a range from 1 meter to 2.5 meters.

• The tree will be approximately 3.71 meters tall after 5 years, with a range of heights from 1 meter to 3.71 meters.

• The tree will be 4.2 meters tall after 5 years, with a range from 1 meter to 4.2 meters.

• The tree will be 5 meters tall after 5 years, with a range from 1 meter to 5 meters.