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?