for 0<=t<=21 the rate of change of the number of black flies on a coastal island at time t days is modeled by R(t)=3sqrt(t)cos(t/3) flies per day. There are 500 flies on the island at the time t=0. To the nearest whole #, what is the max # of flies for 0<=t<=21?

Answer 1

The maximum occurs when R(t) = 0
That would be when t/3 = pi/2
t = 4.712 days

To get the number of flies at that time, you have to integrate R(t) from t=0 to t= 4.712 days, with the number of flies being 500 at t=0

Answer 2

wait...dont u have to integrate it from 0 to 21 or something?? n how would you integrate this equation?