Mastering Exponential Functions: Graphs & Word Problems

1. A bacteria culture doubles in size every hour. If the initial population is 100, what is the domain of the function representing the population over time?

• [0, ∞)

• (-∞, 0)

• [100, ∞)

• [0, 24]

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?

• $12,000

• $8,874

• $10,200

• $15,500

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 representing your balance over time?

• (0, 1)

• (-∞, 0)

• [0, ∞)

• [1, 10]

4. A certain species of fish in a lake grows exponentially. If the population starts at 50 and doubles every month, what is the range of the population after 6 months?

• 1600

• 4000

• 800

• 3200

5. A tree grows exponentially, reaching a height of 2 meters in its first year and doubling its height each subsequent year. What is the domain of the function that models the height of the tree?

• The domain is the set of all integers (0, 1, 2, ...).

• The domain is all real numbers.

• The domain is the set of positive integers (1, 2, 3, ...).

• The domain is the set of negative integers (-1, -2, -3, ...).

6. A city’s population is modeled by the function P(t) = 5000e^(0.03t), where t is the number of years since 2000. What is the range of this function for t between 0 and 20?

• [6000, 9000]

• [5000, 9110.5]

• [5000, 10000]

• [4000, 8000]

7. A radioactive substance decays exponentially. If you start with 80 grams and it loses half its mass every 3 years, what is the domain of the function representing the remaining mass over time?

• (0, 3)

• [0, ∞)

• [3, 80]

• (-∞, 0)

8. A savings account grows exponentially with a formula A(t) = 2000(1.04)^t. What is the range of the account balance after 10 years?

• 2800.50

• 2960.48

• 2500.00

• 3200.75

9. A population of rabbits increases exponentially, starting with 10 rabbits and doubling every month. What is the domain of the function that models the rabbit population over time?

• (0, 12)

• [10, 20]

• [0, ∞)

• (-∞, 0)

10. A smartphone's value decreases exponentially, starting at $800 and losing 20% of its value each year. What is the range of the smartphone's value after 4 years?

• $512.00

• $327.68

• $640.00

• $400.00