Question

An analysis of 8 used trucks listed for sale in the 48076 zip code finds that the power model ln(\hat{price})=3.748-0.1395ln(miles)ln(price^​)=3.748−0.1395ln(miles), for price (in thousands of dollars) and miles driven (in thousands), is an appropriate model of the relationship. If a used truck has been driven for 47,000 miles, which of the following is closest to the predicted price for the truck?(A) $9.46(B) $24.80(C) $3,210.00(D) $9,460.00(E) $24,800.00

Answer 1

(E) $24,800.00

Explanation:

`ln(\hat{price})=3.748-0.1395ln(miles)`

If a used truck has been driven for 47,000 miles

Miles=47 (in thousands)

We therefore have:

`ln(\hat{price})=3.748-0.1395ln(47)\\ln(\hat{price})=3.2109\\$Take the exponential of both sides\\e^{ln(\hat{price})}=e^(3.2109)\\Price=e^(3.2109)\\$Price=24.80 \\Since the price is in thousands of dollars\\Price=24.80 X \$1000\\Predicted Price=\$24800.00`

The correct option is E.