Question

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 point)
The distance that you have left to travel is
miles.
Remaining Attempts : 3

Answer 1

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

Now, let's calculate:

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

Calculate \( 65 \cdot 312 \):

\[ 65 \cdot 312 = 20280 \]

Now substitute this value back into the equation:

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

Calculate:

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

Thus, the distance left to travel to Bloomsfield after 312 hours is

\[ -19840 \text{ miles}. \]

Since a negative distance doesn’t make sense in this context, it means that you have already passed Bloomsfield by 19840 miles. If asked specifically for the remaining distance to Bloomsfield, the interpretation is that you are 19840 miles past it.

So the final answer is:

\[ \text{The distance that you have left to travel is } -19840 \text{ miles.} \]