If the rate of change of a population is given by dP/dt= 3.1(P-2)(P-10), P0, for what values of P is the population increasing?

Question

If the rate of change of a population is given by dP/dt= 3.1(P-2)(P-10), P>0, for what values of P is the population increasing?

anonymous · Answer

it is decreasing over the intervals where the derivative is negative

anonymous · Answer

Can you walk me through?

misty1212 · Answer

HI!!

misty1212 · Answer

do you know how to solve 
$$(p-2)(p-10)<0$$?

misty1212 · Answer

not too hard since it is already in factored form
it is equal to zero at $p=2$ and at $p=10$
since this is a parabola that opens up, it is negative between the zeros and positive outside of them

anonymous · Answer

yes

anonymous · Answer

so what do you do next ?

anonymous · Answer

you are done, there is nothing left to do
it is negative on the interval $(2,1)$ and positive elsewhere

anonymous · Answer

oops i meant negative on the interval $(2,10)$