- #1

AngusYoung93

- 5

- 0

## Homework Statement

The Gompertz equation

dP/dt = P(a - b ln(P))

where a and b are positive constants, is another model of population growth.

a) Find the solution of this differential equation that satisfies the initial condition: P(0) = p(sub(0))

b) What happens to P(t) as t -> infinity?

c) Determine the concavity of the graph of P

**2. The attempt at a solution**

dP/dt = P(a - bQ)

where Q = ln(x)

## Homework Statement

the differential equation

dP/dt = P(10^-1 - (10^-5)P)

models the population of a certain community. Assume P(0) = 2000 and time t is measured in months.

a) Find P(t) and show that lim t -> infinity exists

b) Find the limit

**2. The attempt at a solution**

I do not even know where to start on this. Any help at all would be nice.