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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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.