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?

Answer 1

it is decreasing over the intervals where the derivative is negative

Answer 2

Can you walk me through?

Answer 3

HI!!

Answer 4

do you know how to solve
\[(p-2)(p-10)<0\]?

Answer 5

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

Answer 6

yes

Answer 7

so what do you do next ?

Answer 8

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

Answer 9

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