A population of fish containing P0 fish is introduced into an aquafarm (a lake used to farm fish). Due to unsanitary conditions, the population immediately starts dying off. The fish die off at a rate inversely proportional to the cube root of the existing population. In an attempt to save the population, additional fish are introduced into the aquafarm at a rate proportional to the difference between the existing population and the initial population. Even with these measures, the population never manages to return to its initial level. Write the IVP for the population of fish P(t). All symbolic constants in your DE must represent positive numbers. Justify the signs of each term in your DE.