Graphing and Interpreting Exponential Growth Scenarios

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, 24]

• [100, ∞)

• (-∞, 0)

• [0, ∞)

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

• $5,000.00

• $15,000.00

• $12,000.00

• Approximately $8,874.07

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

• {0, 1, 2, ...}

• {0, 0.5, 1, ...}

• {0, 1, 2, 3, 4, 5}

• {1, 2, 3, ...}

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, ∞)

• (0, ∞)

• (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^(0.5t). What is the domain of this function?

• [0, ∞)

• (0, 100)

• (-∞, 0)

• [100, 200]

6. A tree's height can be modeled by the function H(t) = 10(2^t), where t is the number of years since it was planted. What is the range of this function?

• (0, ∞)

• (10, 20)

• [0, 10]

• (-∞, 0)

7. A company’s profit can be modeled by the function P(t) = 500(1.1^t), where t is the number of years since the company started. What is the domain of this function?

• (0, 10)

• [0, ∞) or t >= 0

• [10, 20]

• (-∞, 0)

8. The amount of radioactive substance remaining after t years can be modeled by A(t) = 100(0.5^t). What is the range of this function?

• (0, 100)

• (0, 50]

• [0, 100]

• (0, 100]

9. A city’s population is projected to grow according to the function P(t) = 1,000(1.03^t). What is the domain of this function in terms of time?

• (0, 10)

• [0, 10]

• [0, ∞)

• (-∞, 0)

10. A savings account grows according to the function S(t) = 2000(1.04^t). If t represents the number of years, what is the range of this function?

• [0, 2000)

• [2000, ∞)

• (2000, 5000)

• [2000, 10000]