First order differential equations (integrating factor)
7
Express \(\frac { 1 } { x } + \frac { 1 } { A - x }\) as a single fraction.
The population of fish in a lake is modelled by the differential equation
\(\frac { d x } { d t } = \frac { x ( 400 - x ) } { 400 }\)
where \(x\) is the number of fish and \(t\) is the time in years.
When \(t = 0 , x = 100\).
In this question you must show detailed reasoning.
Find the number of fish in the lake when \(t = 10\), as predicted by the model.