Question

Raheem is on the road trip from Ohio to Vermont, a distance about 700 miles. During the first two hours of this trip, his distance from Vermontis given by the function x(t)= 700-30t-15t^2. Write a rational function that expresses the average rate of change of Raheem's distance from Vermont during during the first t hours of his trip.

​

Answer 1

d. None of these.

Explanation:

So we are given that in 0 hours he is 700 miles away.

We are given in 2 hours he complete a distance of
`700-30t-15t^2` miles away.

The rate of change is the change in distance over the change in time.

So we are simplifying the following:

`((700-30t-15t^2)-700)/(2-0)`

`(-30t-15t^2)/(2-0)`

`(-30t)/(2)-(15t^2)/(2)`

`-15t-(15)/(2)t^2`

The answer is d. None of these.

Answer 2

d. none of these

Explanation:

The average rate of change of x(t) over the interval [0, t] is given by ...

average rate of change = (x(t) -x(0))/(t-0)

= ((700 -30t -15t^2) -(700))/t

= (-30t -15t^2)/t

= -30 -15t . . . . . . . . . neither version of this answer matches any choice