Question
1. A car decreases in value after a given number of years. The following function represents the value of the car in dollars with respect to its age, x, in years: f (x) = 35,000(.85)^x. Use the input-output table to determine the value of the car after 5 years. Round your answer to the nearest cent.
Years, X: 1, 2, 3, 4, 5
value of Car, F(x): 29,750.00, 25, 287.50, 21, 494.38, 18,270.22, _________
Rounded to the nearest cent, after 5 years, the value of the car will equal $ ___.
Years, X: 1, 2, 3, 4, 5
value of Car, F(x): 29,750.00, 25, 287.50, 21, 494.38, 18,270.22, _________
Rounded to the nearest cent, after 5 years, the value of the car will equal $ ___.
Answers
GPT-4o mini
To find the value of the car after 5 years using the function \( f(x) = 35,000(0.85)^x \), we will substitute \( x = 5 \) into the equation.
1. Substitute \( x = 5 \):
\[
f(5) = 35,000(0.85)^5
\]
2. Calculate \( (0.85)^5 \):
\[
(0.85)^5 = 0.4437053125
\]
3. Now, substitute this value back into the function:
\[
f(5) = 35,000 \times 0.4437053125
\]
4. Perform the multiplication:
\[
f(5) = 15,029.67609375
\]
5. Round to the nearest cent:
\[
f(5) \approx 15,029.68
\]
So, the value of the car after 5 years, rounded to the nearest cent, is $15,029.68.
1. Substitute \( x = 5 \):
\[
f(5) = 35,000(0.85)^5
\]
2. Calculate \( (0.85)^5 \):
\[
(0.85)^5 = 0.4437053125
\]
3. Now, substitute this value back into the function:
\[
f(5) = 35,000 \times 0.4437053125
\]
4. Perform the multiplication:
\[
f(5) = 15,029.67609375
\]
5. Round to the nearest cent:
\[
f(5) \approx 15,029.68
\]
So, the value of the car after 5 years, rounded to the nearest cent, is $15,029.68.