SOLUTION: 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 c
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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?
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
the population with a certain disease for the time is determined by the function
Critical points , and , are points where the function is defined and its derivative is or.
When is the population a maximum?
max:
'
at =>
and
=>
then
Global Maximum is at (, )
Global Minimum is at (,)
When is the disease will cease?
the disease will cease at
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