The rabbit population on a small island is given by the function below, where t is the time in months since observation of the rabbit population began.

P(t)=110t-0.4t^4+1000
What is the maximum population? Please show work.

Question

The rabbit population on a small island is given by the function below, where t is the time in months since observation of the rabbit population began.

P(t)=110t-0.4t^4+1000
What is the maximum population? Please show work.

hero · Answer

Well, you could simply graph the function to find it's max value.

hero · Answer

You could also take the derivative of the function too.

a_clan · Answer

find the maxima

hero · Answer

John, do you still need help with this?

anonymous · Answer

equation rewrite p(t)= -.4t^4 + 110t +1000
p'(t)= -1.6t^3 + 110
maximum and min is where this equation = 0
0=-1.6t^3 + 110
1.6t^3=110
t^3 =68.75
t=4.0966

anonymous · Answer

looks about right in graph form

hero · Answer

hobeau, you found the point where the slope of p(t) = 0. You didn't find the actual max.