Finding Domain & Range 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, 200]

• [-∞, 0)

• [0, ∞)

• (0, 10]

2. The height of a plant grows exponentially, modeled by the function h(t) = 5e^(0.3t), where t is time in weeks. What is the range of this function?

• (-∞, 0)

• [0, 5]

• (5, 10)

• (0, ∞)

3. A car's value decreases exponentially over time, modeled by V(t) = 20000(0.85)^t. What is the domain of this function?

• [0, ∞)

• (-∞, 0)

• (0, 20000)

• [0, 20000]

4. The amount of a radioactive substance decreases exponentially. If the initial amount is 50 grams, what is the range of the function after t years?

• (0, 0)

• (50, 100]

• (0, 100)

• (0, 50]

5. A bank account earns interest modeled by A(t) = 1000(1.05)^t. What is the domain of this function in terms of time?

• (0, 10]

• (-∞, 0)

• [0, ∞)

• [0, 10]

6. The number of users on a social media platform grows exponentially, modeled by U(t) = 200(1.1)^t. What is the range of this function?

• (0, 200)

• (200, ∞)

• (0, ∞)

• (-∞, 0)

7. A tree's height can be modeled by the function H(t) = 2(3^t), where t is the age of the tree in years. What is the domain of this function?

• [0, ∞)

• (-∞, 0)

• (0, 10)

• [0, 10]

8. The value of a car after t years is given by V(t) = 30000(0.9)^t. What is the range of this function?

• (0, 100000]

• (0, 30000]

• [0, 30000]

• (0, 30000)

9. A certain species of fish in a lake grows exponentially, modeled by F(t) = 50e^(0.2t). What is the domain of this function?

• (0, 100)

• [0, ∞)

• (-10, 10)

• (-∞, ∞)

10. The amount of money in an investment account grows according to the function I(t) = 1500(1.07)^t. What is the range of this function?

• (1500, ∞)

• [0, 1500]

• [1500, ∞)

• (0, 1500)