Question

The distance away from the city of Bloomfield is a function of time. The function D(h)=440−65h represents the distance in miles away from Bloomfield 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) The distance that you have left to travel is miles.

Answer 1

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

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

Calculating \( 65 \times 312 \):

\[ 65 \times 312 = 20280 \]

Now substituting this back into the equation:

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

Calculating the result:

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

Since the distance cannot be negative, this indicates that after traveling for 312 hours, you have exceeded the distance to Bloomfield. Therefore, rather than "distance left," we could say you've traveled past Bloomfield by 19840 miles.

Thus, the distance that you have left to travel is \( \text{-19840} \) miles, or you can state that you are 19840 miles past Bloomfield.