# calculus

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for 0<=t<=21 the rate of change of the number of blakc 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?

• calculus -

R = 3√t cos(t/3)
R' = 3/2√t cos(t/3) - √t sin(t/3)
R' = 0 when

3/2√t cos(t/3) = √t sin(t/3)
3cos(t/3) = 2t sin(t/3)
3/2 cot(t/3) = t
t = 1.96, 9.88, 19.08

not sure how there are 500 flies at t=0. That doesn't fit R(t). Anyway, if that can be fixed, just plug in those values for t to get what you need.

• calculus -

wait..dont u hve to integrate it?

• calculus -

oops. yes. I misread the problem. Didn't see the "rate of change" phrase.

• calculus -

wait..so how would you integrate that equation..im hving trouble with tht..

• calculus -

Beats me. It doesn't use standard elementary functions. Are you studying numerical methods?

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