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?

Question

Mathematics

Chef

1 November, 13:47

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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Answers (1)

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Ronnie Shepard · 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.

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 ofh' (t) = 0.2t2/3 + vt ft/yrIf the tree was 2 feet tall when it was planted, how tall will it be in 27 years?

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?