Question

The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h
𝐷
(
ℎ
)
=
440
−
65
ℎ
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
3
1
2
hours of traveling. Enter your response in decimal form.(1 point)
The distance that you have left to travel is miles blank.

Answer 1

To find the distance left to get to Bloomsfield after \( h = 312.5 \) hours of traveling, we can substitute this value into the function \( D(h) = 440 - 65h \).

Let's perform the calculation:

\[
D(312.5) = 440 - 65 \times 312.5
\]

Calculate \( 65 \times 312.5 \):

\[
65 \times 312.5 = 20312.5
\]

Now substitute that back into the equation:

\[
D(312.5) = 440 - 20312.5 = 440 - 20312.5 = -19872.5
\]

Since the distance cannot be negative, this means that after traveling for 312.5 hours, you would have already passed Bloomsfield. Thus, the distance left to get to Bloomsfield is:

\[
\text{Distance left to travel} = -19872.5 \text{ miles}
\]

This indicates that you are 19,872.5 miles past Bloomsfield.

However, if the context of the question requires only the absolute value of distance:

The distance that you have left to travel is \( 19872.5 \) miles.