Modeling and Analyzing Exponential Growth and Decay

1. A bacteria culture doubles in size every 3 hours. If the initial population is 500, create an exponential function model to represent the population after t hours. What will the population be after 12 hours?

• 6000

• 10000

• 8000

• 4000

2. The value of a car decreases by 20% each year. If the car's initial value is $20,000, create an exponential function to model its value over time. What will the value be after 5 years?

• $4,000.00

• $10,000.00

• $8,000.00

• $6,553.60

3. A certain investment grows at an annual rate of 5%. If you invest $1,000, create an exponential function to model the investment's value after t years. How much will it be worth after 10 years?

• $1,200.00

• $2,000.00

• $1,628.89

• $1,500.00

4. The table below shows the population of a town over 5 years. Analyze the data and determine if the population is growing exponentially. Year: 0, Population: 1,000; Year: 1, Population: 1,200; Year: 2, Population: 1,440; Year: 3, Population: 1,728; Year: 4, Population: 2,073. What is the growth factor?

• 1.5

• 1.8

• 1.2

• 2.0

5. A tree grows at a rate of 10% per year. If its height is currently 2 meters, create an exponential function to model its height over time. How tall will the tree be in 4 years?

• 2.93 meters

• 3.5 meters

• 4.2 meters

• 1.8 meters

6. The table below shows the amount of a radioactive substance remaining over time. Analyze the data to find the decay constant. Time (years): 0, Amount: 100g; Time: 1, Amount: 90g; Time: 2, Amount: 81g; Time: 3, Amount: 73g. What is the exponential decay model?

• A(t) = 100 * e^(0.1054t)

• A(t) = 100 * e^(-0.05t)

• A(t) = 100 * e^(-0.2t)

• A(t) = 100 * e^(-0.1054t)

7. A population of fish in a lake is modeled by the function P(t) = 200e^(0.3t), where t is the time in years. What will the population be after 5 years?

• 500

• 1200

• 750

• 896

8. A savings account earns interest compounded continuously at a rate of 4%. If you deposit $500, create an exponential function to model the amount in the account after t years. How much will be in the account after 3 years?

• 550.00

• 600.00

• 563.75

• 575.25

9. The number of users of a new app is modeled by the function U(t) = 150(1.5)^t, where t is the number of months since launch. How many users will there be after 6 months?

• 1709

• 1500

• 2000

• 1200

10. A scientist is studying a species of plant that grows exponentially. The initial count of plants is 50, and it doubles every month. Create a table showing the number of plants for the first 6 months and determine the exponential growth function.

• Month 0: 50, Month 1: 100, Month 2: 200, Month 3: 300, Month 4: 400, Month 5: 500, Month 6: 600

• Month 0: 50, Month 1: 100, Month 2: 250, Month 3: 500, Month 4: 1000, Month 5: 2000, Month 6: 4000

• Month 0: 50, Month 1: 100, Month 2: 200, Month 3: 400, Month 4: 800, Month 5: 1600, Month 6: 3200

• Month 0: 50, Month 1: 150, Month 2: 300, Month 3: 600, Month 4: 1200, Month 5: 2400, Month 6: 4800