Question

An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after t years is changing at the rate of

h'(t) = 0.2t2/3 + vt ft/yr


If the tree was 2 feet tall when it was planted, how tall will it be in 27 years?

Answer 1

The equation describing the rate of change of the height of tree is given by
h'(t) = 0.2t²/3 + vt

We are given an initial condition that
h = 0, t = 0
and we are asked to solve for the value of h when t = 27

The given equation can be integrated using the given limits to solve for h at t =27.