Question

Integrated Parts of Exponential Functions HW Write an exponential function for the following problems: 1. You put $4500 into a savings account which earns 5% interest. 2. You bought a car for $9750 and it depreciates 8% each year. 3. Walnut Cove has a population of 87,500 people and is growing exponentially at a rate of 2% each year. 4. Your grandfather’s house is currently worth $120,000 but is depreciating at a rate of 13% each year. State the starting value and whether it is decreasing or increasing and by what percent for the following problems: 5. P = 2500(0.9)t 6. P = 1200(1.185)t 7. P = 800(0.78)t 8. P = 600(1.12)t

Answer 1

The answers to the following problems are;

1. It is increasing at 5% per year.

2. It is decreasing at 8% per year.

3. It is increasing at 2% per year.

4. It is decreasing at 13% per year.

5. It is decreasing at 10% per year.

6. It is increasing at 18.5% per year.

7. It is decreasing at 22% per year.

8. It is increasing at 12% per year.

Writing the exponential functions for the problems.

1. Savings Account:

Function: P(t) = 4500(1.05)ᵗ

Starting value: $4500

Increasing: Yes, at 5% per year

2. Car Depreciation:

Function: V(t) = 9750(0.92)ᵗ

Starting value: $9750

Decreasing: Yes, at 8% per year

3. Walnut Cove Population:

Function: P(t) = 87500(1.02)ᵗ

Starting value: 87,500 people

Increasing: Yes, at 2% per year

4. Grandfather's House:

Function: V(t) = 120000(0.87)ᵗ

Starting value: $120,000

Decreasing: Yes, at 13% per year

5. P = 2500(0.9)ᵗ

Starting value: $2500

Decreasing: Yes, at 10% per year (1 - 0.9 = 0.1)

6. P = 1200(1.185)ᵗ

Starting value: $1200

Increasing: Yes, at 18.5% per year (1.185 - 1 = 0.185)

7. P = 800(0.78)ᵗ

Starting value: $800

Decreasing: Yes, at 22% per year (1 - 0.78 = 0.22)

8. P = 600(1.12)ᵗ

Starting value: $600

Increasing: Yes, at 12% per year (1.12 - 1 = 0.12)