The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65h

Question

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 7/2 hours of traveling. Enter your response in decimal form

Answer 1

To find the distance left to get to Bloomsfield after \( \frac{7}{2} \) hours of traveling, we can use the distance function \( D(h) = 440 - 65h \).

First, we substitute \( h = \frac{7}{2} \) into the function:

\[ D\left(\frac{7}{2}\right) = 440 - 65\left(\frac{7}{2}\right) \]

Calculating \( 65\left(\frac{7}{2}\right) \):

\[ 65\left(\frac{7}{2}\right) = \frac{65 \times 7}{2} = \frac{455}{2} = 227.5 \]

Now substitute this value back into the distance function:

\[ D\left(\frac{7}{2}\right) = 440 - 227.5 \] \[ D\left(\frac{7}{2}\right) = 212.5 \]

Therefore, the distance left to get to Bloomsfield after \( \frac{7}{2} \) hours of traveling is:

\[ \boxed{212.5} \text{ miles} \]