Answer:
[tex]D(21) = 1.612\ ft[/tex]
Step-by-step explanation:
The question has missing details;
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex]
Given that t = 21
Solve for Diameter, D
To do this, we simply substitute 21 for t in the above function
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex] becomes
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.21 }}[/tex]
Solve for [tex]e^{-0.21}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9* 0.81058424597}[/tex]
Simplify the denominator
[tex]D(21) = \frac{5.4}{1+2.35069431331}[/tex]
[tex]D(21) = \frac{5.4}{3.35069431331}[/tex]
[tex]D(21) = 1.61160628069[/tex]
[tex]D(21) = 1.612\ ft[/tex] (Approximated)
Hence, the diameter of the 21 year old tree is 1.612 feet
