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I would love a solution and an explanation for the following question! The size of a fish varies in time according to the law

`(dV)/(dt)=-V+(1)/(10)S,`

where

`V`

is the volume of the fish and

`S`

is its surface area. For a particular species, the volume and surface area are related to the length of the fish

`L`

(in metres) according to

`V=(L^(3))/(10), and ,S=L^(2).`

(a) Show that

`L`

satisfies the differential equation

`(dL)/(dt)=(1)/(3)(1-L).`

(b) Solve this equation as a linear differential equation to find

`L(t)`

given that

`L=0`

when

`t=0`

. (c) What is the maximum size to which such a fish can grow? (d) If

`t`

is measured in years, how long does it take for a fish to grow to

`50cm`

in length?