Mathematics: For a certain type of tree the diameter D (in feet) depends on the tree s age t (in years) according to the logistic growth model. Find the diameter of a 21-year-old tree. Please give the answer to three decimal places.

For a certain type of tree the diameter D (in feet)

nadiareese

30.01.2022

$D(21) = 1.612\ ft$

Step-by-step explanation:

The question has missing details;

$D(t) = \frac{5.4}{1+2.9e^{-0.01t}}$

Given that t = 21

Solve for Diameter, D

To do this, we simply substitute 21 for t in the above function

$D(t) = \frac{5.4}{1+2.9e^{-0.01t}}$ becomes

$D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}$

$D(21) = \frac{5.4}{1+2.9e^{-0.21 }}$

Solve for $e^{-0.21}$

$D(21) = \frac{5.4}{1+2.9* 0.81058424597}$

Simplify the denominator

$D(21) = \frac{5.4}{1+2.35069431331}$

$D(21) = \frac{5.4}{3.35069431331}$

D(21) = 1.61160628069

$D(21) = 1.612\ ft$ (Approximated)

Hence, the diameter of the 21 year old tree is 1.612 feet

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