Solving Real-World Problems with Exponential Functions

1. A population of bacteria doubles every 3 hours. If the initial population is 100, what is the domain of the function representing the population over time?

• [-∞, 0)

• [100, 200]

• (0, 10]

• [0, ∞)

2. The value of a car depreciates exponentially. If a car is worth $20,000 and loses 15% of its value each year, what is the range of the car's value after 5 years?

• $8,874

• $12,000

• $15,500

• $10,200

3. A bank offers an account that compounds interest exponentially. If you deposit $1,000 at an interest rate of 5% per year, what is the domain of the function that models the account balance over time?

• (-∞, 0)

• [0, 10]

• (0, 10)

• [0, ∞)

5. The height of a plant grows exponentially. If it starts at 2 cm and grows to 50 cm in 4 weeks, what is the domain of the growth function?

• [0, 10]

• [0, 4]

• [0, 50]

• [2, 4]

6. A certain investment grows exponentially. If you invest $500 and it grows to $1,500 in 6 years, what is the range of the investment's value?

• $1,000 to $2,000

• $500 to $1,500

• $1,500 to $2,500

• $500 to $2,000

7. A viral video on a social media platform gains views exponentially. If it starts with 200 views and doubles every day, what is the domain of the function representing the views over time?

• t < 0, where t is a negative integer

• t is any real number

• t >= 0, where t is a non-negative integer

• t >= 1, where t is a positive integer

8. The temperature of a cooling object decreases exponentially. If it starts at 100°C and cools to 25°C in 10 minutes, what is the range of the temperature function?

• [10, 100]

• [25, 50]

• [25, 100]

• [0, 100]

9. A tree's height increases exponentially. If it is currently 1 meter tall and grows to 10 meters in 5 years, what is the domain of the height function?

• [0, 1]

• [0, 5]

• [1, 5]

• [0, 10]

10. A savings account grows exponentially with a fixed interest rate. If you start with $2,000 and it grows to $5,000 in 8 years, what is the range of the account balance?

• $3,000 to $7,000

• $2,500 to $6,000

• $2,000 to $5,000

• $1,000 to $5,000