Question

The distance away from the city of Bloomsfield is a function of time. The function D(h) = 440 − 65h represents the distance in miles away from Bloomsfield as you travel toward the city, based on the number of hours, h , you have traveled. Find the distance left to get to Bloomsfield after 312 hours of traveling. Enter your response in decimal form.

Answer 1

To find the distance left to get to Bloomsfield after 312 hours of traveling using the given function \( D(h) = 440 - 65h \), we can substitute \( h = 312 \) into the function.

\[
D(312) = 440 - 65 \times 312
\]

Now, we calculate \( 65 \times 312 \):

\[
65 \times 312 = 20280
\]

Next, we substitute this value back into the distance function:

\[
D(312) = 440 - 20280
\]

Now calculate \( 440 - 20280 \):

\[
D(312) = 440 - 20280 = -19840
\]

Therefore, the distance left to get to Bloomsfield after 312 hours of traveling is

\[
\boxed{-19840}
\]

This negative result indicates that the distance traveled exceeds the starting distance to Bloomsfield, meaning that after 312 hours, you would have traveled past Bloomsfield by 19840 miles.