Secant Lines and Average Rates of Change

Question

The function H(t)=10t√ gives the height in feet of a hot air balloon after t seconds. Find the average rate of change from t=1 to t=9.

Answer 1

The average rate of change of a function f over an interval an interval a<t<b is given by (f(a)-f(b))/(a-b). Your function is H(t) = 10√t and your interval is 1≤t≤9. Thus the average rate of change is (10√1 - 10√9)/(1-9) = (10-30)/(-8) = 20/8 = 2.5. The average rate of change of the height of the balloon between t=1 and t=9 seconds is 2.5 feet/second.