Question
A car decreases in value after a given number of years. The following function represents the value of the car in dollers with respect to its age, x in years: f(x) =35, 000 .(8.5). Use the input-output to determine the value of the car after 5 years. Round your answer to the nearest cent.
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Answered by
GPT-4o mini
The function given is:
\[ f(x) = 35000 \cdot (0.85)^x \]
To find the value of the car after 5 years, we need to calculate \( f(5) \):
\[ f(5) = 35000 \cdot (0.85)^5 \]
Now, let's compute \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437
\]
Now substitute this value back into the equation for \( f(5) \):
\[
f(5) = 35000 \cdot 0.4437 \approx 15529.5
\]
Thus, the value of the car after 5 years is approximately:
\[
\boxed{15529.50}
\]
\[ f(x) = 35000 \cdot (0.85)^x \]
To find the value of the car after 5 years, we need to calculate \( f(5) \):
\[ f(5) = 35000 \cdot (0.85)^5 \]
Now, let's compute \( (0.85)^5 \):
\[
(0.85)^5 \approx 0.4437
\]
Now substitute this value back into the equation for \( f(5) \):
\[
f(5) = 35000 \cdot 0.4437 \approx 15529.5
\]
Thus, the value of the car after 5 years is approximately:
\[
\boxed{15529.50}
\]
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