Question 1194793
the population with a certain disease for the time 0 < t < 20 is determined by the function p(t) = 1/100 (20t^3 - t^4). When is the population a maximum? When is the disease will cease?
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p(t) = 1/100 (20t^3 - t^4)
p'(t) = (1/100)*(60t^2 - 4t^3)  1st derivative
(1/100)*(60t^2 - 4t^3) = 0
60t^2 - 4t^3 = 0
t^2*(60 - 4t) = 0
t = 15 is the max
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p(t) = 1/100 (20t^3 - t^4) = 0
(20t^3 - t^4) = 0
t^3*(20-t) = 0
p(t) = 0 at t=0 and at t=20