Thread: 3 calculus things im stuck on

formula y= (y0*L)/[y0+(L-y0)e^-kt]

1.) when looking at a graph of a function, how do i estimate the value of k?


2.) suppose that the growth of a population y=y(t) is given by the logistic equation y= (1000)/(1+999e^-.9t)
when does the population reach 75% of the carrying capacity?
so far i have:
y= (750)/(1+999e^-.9t)
e^-.9t= (750-y)/(999y)
t= -.9ln[(750-y)/(999y)]
but what do i plug in for y?


3.)suppose that a population y(t) grows in accordance with the logistic model dy/dt= 50y-.0001y^2
what is the value of k?
for what value of y is the population growing most rapidly?

hmm is this first order differential equations?