3. Exponential Functions in Context(1 point)

Question

Markus bought a car for $40,000
and it decreases in value by 15%
every year.

Part A: Write an exponential function that represents the value of the car at the end of every year. Use the variable x
in your equation. Do not include a comma in your equation. Simplify the expression in the parenthesis.

f(x)=


Part B: Fill out the table that represents the value of the car after x
years. Do not include a comma in your response. Write your answer to the nearest cent, write ".00" if there are no cents.

x
f(x)

0 $
1 $
3 $
5 $
8 $
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Answer 1

Part A: Exponential Function

To represent the value of the car after x years, we start with the initial value of the car, which is $40,000. The car depreciates at a rate of 15% per year, which means it retains 85% of its value each year.

The exponential function can be formulated as follows:

\[ f(x) = 40000(0.85)^x \]

Part B: Values of the Car After x Years

To fill out the table for the values of the car after x years, we can calculate \(f(x)\) for each value of \(x\):

1. When \(x = 0\): \[ f(0) = 40000(0.85)^0 = 40000(1) = 40000.00 \]

2. When \(x = 1\): \[ f(1) = 40000(0.85)^1 = 40000(0.85) = 34000.00 \]

3. When \(x = 3\): \[ f(3) = 40000(0.85)^3 \approx 40000(0.614125) \approx 24565.01 \]

4. When \(x = 5\): \[ f(5) = 40000(0.85)^5 \approx 40000(0.443705) \approx 17748.20 \]

5. When \(x = 8\): \[ f(8) = 40000(0.85)^8 \approx 40000(0.272490) \approx 10899.61 \]

Completed Table

| x | f(x) | |-----|----------| | 0 | 40000.00 | | 1 | 34000.00 | | 3 | 24565.01 | | 5 | 17748.20 | | 8 | 10899.61 |