Question

A function is given.
f(t)=3t square, t=5,t=5+h
(a) Determine the net change between the given values of the variable.


(b) Determine the average rate of change between the given values of the variable.

Answer 1

To determine the net change between the given values of the variable, we need to find the difference between f(t=5) and f(t=5+h).

(a) Net change: f(t=5+h) - f(t=5)
= (3(5+h)^2) - (3(5)^2)
= (3(25+10h+h^2)) - (3(25))
= 75 + 30h + 3h^2 - 75
= 30h + 3h^2

Therefore, the net change between the given values is 30h + 3h^2.

(b) To find the average rate of change between the given values, we need to divide the net change by the change in t.

Average rate of change = (30h + 3h^2)/h
= 30 + 3h

Therefore, the average rate of change between the given values is 30 + 3h.