Exponential Functions: Solving & Ranges in Real Life

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

• 800

• The population after 12 hours is 1600.

• 1200

• 2000

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

• $15,000 after 5 years

• $5,000 after 5 years

• The value of the car after 5 years is approximately $8,874.00.

• $10,500 after 5 years

4. The height of a plant grows exponentially, reaching 1 meter in 4 days. If the growth continues at the same rate, how tall will the plant be after 16 days? Determine the range of the plant's height function.

• 10 meters

• 8 meters

• 4 meters

• 2 meters

5. A radioactive substance decays exponentially. If you start with 80 grams and it decays to half its amount every 5 years, how much will remain after 15 years? What is the range of the substance's mass over this time?

• 15 grams

• 5 grams

• 20 grams

• 10 grams

7. The number of views on a viral video increases exponentially. If it starts with 1,000 views and doubles every week, how many views will it have after 6 weeks? Determine the range of views over this period.

• 64000

• 32000

• 50000

• 128000

8. A tree's height increases exponentially, reaching 3 meters in 5 years. If this growth rate continues, what will the height be after 15 years? What is the range of the tree's height function?

• Approximately 15 meters

• Approximately 20.09 meters

• Approximately 25 meters

• Approximately 10 meters

9. A certain species of fish in a lake grows exponentially. If the initial population is 200 and it doubles every year, what will the population be after 4 years? Determine the range of the fish population function.

• 4000

• 1600

• 2400

• 3200

10. A smartphone's battery life decreases exponentially. If it starts with a full charge of 100% and loses 20% of its charge every hour, how much charge will be left after 5 hours? What is the range of the battery charge function?

• 75%

• 50%

• 32.77%

• 10%