The Pacific Halibut Fishery Has Been Modeled by the Differential $\frac { d y } { d t } = k y \left( 1 - \frac { y } { K } \right)$

The Pacific halibut fishery has been modeled by the differential equation $\frac { d y } { d t } = k y \left( 1 - \frac { y } { K } \right)$ 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 $M = 40 \times 10 ^ { 4 } \mathrm {~kg}$ and $k = 0.02$ per year. If $y ( 0 ) = 5 \times 10 ^ { 4 }$ , find the biomass a year later.

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