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?