Identifying Domains and Ranges in 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?

• [100, ∞)

• (-∞, 0)

• [0, 24]

• [0, ∞)

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

• $12,000.00

• $8,874.07

• $10,500.00

• $15,000.00

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

• [0, ∞)

• (-∞, 0)

• (0, 10)

• [0, 10]

4. A certain species of fish in a lake grows exponentially. If the fish population is modeled by the function P(t) = 50e^(0.3t), where t is time in years, what is the range of this function?

• (0, 50]

• (50, ∞)

• [50, ∞)

• [0, 50]

5. A researcher is studying the spread of a virus. The number of infected individuals can be modeled by the function I(t) = 200e^(0.4t). What is the domain of this function?

• (0, 200)

• [200, ∞)

• [0, ∞)

• (-∞, 0)

6. A tree grows exponentially, reaching a height of 10 feet in 5 years. If the height can be modeled by H(t) = 10(1.5)^t, what is the range of the function after 10 years?

• [0, 10]

• [10, 100]

• [10, 300]

• [10, 576.65]

7. The amount of a radioactive substance decreases exponentially. If you start with 80 grams and it halves every 4 years, what is the domain of the function modeling the remaining substance?

• (-∞, 0)

• [0, 80]

• [0, ∞)

• (0, ∞)

8. A savings account grows exponentially with a formula A(t) = 500(1.04)^t. If t represents the number of years, what is the range of this function after 10 years?

• (0, 500]

• (0, 1000]

• (0, 600.50]

• (0, 740.12]

9. A company’s profit is modeled by the function P(t) = 300e^(0.1t). If t is the number of years since the company started, what is the domain of this function?

• [0, ∞)

• (-∞, 0)

• (0, 10)

• [10, 20]

10. The height of a plant is modeled by the function H(t) = 2e^(0.5t). If t is in weeks, what is the range of the function after 8 weeks?

• H(8) ≈ 109.196

• H(8) ≈ 90.789

• H(8) ≈ 50.123

• H(8) ≈ 75.456