P(t)=800/1+9e-0.9t'

P(t) represents the population size at time t, and the logistic growth model is given by:

P(t) = K / (1 + A e^(-rt))

where K is the carrying capacity, A is the initial population size, r is the growth rate, and t is time.

Comparing this with the given equation:

P(t) = 800 / (1 + 9 e^(-0.9t))

We can see that:

K = 800
A = 0 (since there is no initial population given)
r = 0.9

Therefore, the logistic growth model for this population is:

P(t) = 800 / (1 + e^(-0.9t))

This model describes how the population size changes over time, starting from an initial population of zero and approaching a maximum carrying capacity of 800. The growth rate is initially high but slows down as the population approaches the carrying capacity.