# models for population growth!!..HELPP!!

• Dec 3rd 2007, 06:25 AM
singh1030
models for population growth!!..HELPP!!
The Pacific halibut fishery has been modeled by the differential equation:
dy/dt=ky(1-(y/K) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t(measured in years), the carrying capacity is estimated to be K=8 x 10^7 kg, and k= 0.71 per year.

a) if y(0)=2 x 10^7 kg, find the biomass a year later.
b) How long will it take for the biomass to reach 4 x 10^7 kg?

HELPP!!
• Dec 3rd 2007, 06:43 AM
topsquark
Quote:

Originally Posted by singh1030
The Pacific halibut fishery has been modeled by the differential equation:
dy/dt=ky(1-(y/K) where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t(measured in years), the carrying capacity is estimated to be K=8 x 10^7 kg, and k= 0.71 per year.

a) if y(0)=2 x 10^7 kg, find the biomass a year later.
b) How long will it take for the biomass to reach 4 x 10^7 kg?

HELPP!!

Basically you need a solution to the differential equation
$\displaystyle \frac{dy}{dt} = ky \left ( 1 - \frac{y}{k} \right )$

$\displaystyle \frac{dy}{dt} = ky \left ( \frac{k - y}{k} \right )$

$\displaystyle \frac{dy}{y(k - y)} = dt$

You can integrate the LHS using partial fractions.

-Dan