Question

data collected about vehicle age and fuel efficiency were used to calculate the model ŷ = 39.54(0.993)^x, where x represents the age of the vehicle in years and ŷ represents the predicted fuel efficiency in miles per gallon. predict the fuel efficiency for a car that is 8 years old. 56.479 miles per gallon, 39.54 miles per gallon, 37.379 miles per gallon, 9.93 miles per gallon

Explanation:

Step1: Identify the values of x and the model

We are given the model $\hat{y}=39.54(0.993)^x$, and $x = 8$ (age of the car is 8 years).

Step2: Substitute x into the model

$\hat{y}=39.54\times(0.993)^8$.
First, calculate $(0.993)^8$. Using a calculator, $(0.993)^8\approx0.9457$.
Then, $\hat{y}=39.54\times0.9457$.
$\hat{y}\approx37.379$.

Answer:

37.379 miles per gallon