The model we are using is $\frac{dp}{dt} = KP(P-M)$. Determine when P=75.
Given a table of years and the populations during those years. Specifically focusing on $1925$ and $1975$ with an h value of 1. Where the respective populations are $25$ and $47.54$. Its growing
Told to use the formula:
$P'(t) = \frac{P(t+h)-P(t-h)}{2h}$ with a step size $h =1$
to approximate $P'(t)$ where $t=1925$ and $t=1975$ I get $P'(25)= .19$ and $P'(75)=.25$
Now plugging those in to get K and M values is a problem
$$P'(75)=KP(P-M)$$ $$.25 =K47.54(47.54-M)$$
Assuming that 47.54K is the same thing as K so it gets absorbed.
$$k = \frac{.25}{47.54-M}$$
Now plugging $K$ back into our population model.
$$.19 = \frac{.25}{47.54-M}(25)(25-M)$$
After doing algebra I get
$$M=37.385$$ but the book says that $M=100$
Well..., you made some kind of algebra/arithmetic mistake because: