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.

1 answer

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

Now, we calculate:

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

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

\[ 65 \times 312 = 20280 \]

Now we substitute this back into the distance function:

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

Now we calculate:

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

Since a negative distance does not make sense in this context, it indicates that after 312 hours of traveling, you have already passed Bloomsfield by 19840 miles.

Thus, the distance left to get to Bloomsfield is \(-19840\) miles, which suggests you are well past the city. However, if you need the absolute value of the distance past Bloomsfield, that is:

\[ 19840 \text{ miles} \]

In decimal form, that's simply:

\[ 19840.0 \]

So the response is 19840.0 miles (indicating that you are 19840 miles past Bloomsfield).