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.(1 point)

Question

The distance that you have left to travel is miles.

Answer 1

To find the distance left to get to Bloomsfield after traveling for 312 hours, we can evaluate the function \( D(h) = 440 - 65h \) at \( h = 312 \).

Plugging in the value of \( h \):

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

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

\[ 65 \times 312 = 20280 \]

Now substitute this result back into the equation:

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

Calculating that:

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

Since the distance cannot be negative, this means that after 312 hours of traveling, you have already passed Bloomsfield by 19,840 miles.

So, the interpretation would be:

The distance that you have left to travel is negative, indicating that you have overshot your destination by 19,840 miles.

If you just want the "distance left" in decimal form, we would report that as:

\[ \text{Distance left} = -19840 \text{ miles} \]

To clarify, the answer indicates how far beyond Bloomsfield you are, rather than a positive remaining distance.