The information that I am given: p(12)=95,75 ; P(14)=98 ; and the carrying capacity K = 100. Question : What is r, as defined in:
deltaP/P = -r/K * P + r
The answer in the book is 0,325
The closest I have come is 0.388
Please let me know how to solve this problem. Thanks.
This is my working:
My attempt at answer [My answer2
Probably, the best thing to do would be to solve the differential equation and then plug in values of $t$ and $P$.
I believe you forgot a $dt$ in the denominator so I'll add that in.
$\displaystyle \frac{dP}{P\cdot dt} = -\displaystyle \frac{r}{K}(P)+r$
can be rewritten as $\displaystyle \frac{dP}{dt} = rP\left(1-\frac{P}{K}\right)$.
This is the more conventional forme that suggests that growth slows down as population (P) approaches carrying capacity (K).
Anyways, the next step is to solve the equation.
This is a clean solution, taken from https://sites.math.northwestern.edu/~mlerma/courses/math214-2-04f/notes/c2-logist.pdf, and in this example, $r$ is replaced with $k$. They represent the growth factor.
Now, all you have to do is plug in values of $t$ and $P$ and you can solve for $r$. Good luck!