Question

The distance away from the city of Bloomsfield is a function of time. The function D(h)=440−65hrepresents 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 312hours of traveling. Enter your response in decimal form.

Answer 1

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

Let's substitute \( h = 312 \) into the function:

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

Now, calculate \( 65 \times 312 \):

\[ 65 \times 312 = 20280 \]

Now substitute this back into the equation:

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

Calculating the subtraction:

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

Since distance cannot be negative, this indicates that you have gone past Bloomsfield by 19840 miles.

Thus, the distance left to get to Bloomsfield after 312 hours of traveling is -19840 miles.