Understanding 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?

• [0, ∞)

• (0, 10]

• [-∞, 0)

• [100, 200]

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?

• $8,874.14

• $12,000.00

• $5,000.00

• $15,000.00

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, ...}

• {1, 2, 3, ...}

• {0, 1, 2, 3, 4, 5}

• {0, 0.5, 1, ...}

4. A certain species of fish in a lake grows exponentially. If the initial population is 50 and it triples every year, what is the range of the population after 4 years?

• 150

• 4050

• 1000

• 200

5. A researcher is studying the spread of a virus. If the number of infected individuals doubles every week, what is the domain of the function that models the number of infections over time?

• [1, 10]

• (0, 1)

• [0, ∞)

• (-∞, 0)

6. A tree grows exponentially, reaching a height of 2 meters in its first year and doubling its height each subsequent year. What is the range of the height of the tree after 5 years?

• 32 meters

• 40 meters

• 24 meters

• 16 meters

7. A company’s revenue grows exponentially, starting at $10,000 and increasing by 20% each year. What is the domain of the function that represents the revenue over time?

• [0, ∞)

• (0, 10,000)

• (-∞, 0)

• [10,000, ∞)

8. The half-life of a radioactive substance is 10 years. If you start with 80 grams, what is the range of the amount remaining after 30 years?

• 40 grams

• 5 grams

• 10 grams

• 20 grams

9. A savings account earns interest that is compounded continuously. If you start with $500 and the interest rate is 4%, what is the domain of the function that models the account balance?

• [0, ∞)

• [0, 10]

• (-∞, 0)

• (0, 10)

10. A certain type of plant grows exponentially, starting at 5 cm and increasing by a factor of 1.5 each month. What is the range of the plant's height after 6 months?

• 45 cm

• 56.95 cm

• 30 cm

• 70 cm