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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.

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?
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2 h (t) = 0.2t 3 + v.t
Integrating with respect to t, we get
h(t) = 2 0.2t 3 dt + v .tdt + c where c is the integrating constant. We have
h(t) = 0.2 × 3 5
t2
t 3 + v. + c
5
2 t2
0.6 5
t 3 + v. +...

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