If a tree's value (v)is growing according to the equation $v ( t ) = e ^ { . i t - .0025 s t }$ with an interest rate of 5 percent,the tree should be harvested when t =

Question

Quizplus · Accepted Answer

To find the time at which the tree should be harvested, we need to find the maximum value of the equation. Taking the derivative of the equation with respect to time (t), we get:

v'(t) = 88000(0.05)e^(0.05t)

Setting v'(t) = 0 to find the maximum value, we get:

0 = 88000(0.05)e^(0.05t)
0 = e^(0.05t)

Taking the natural logarithm of both sides, we get:

ln(0) = 0.05t
t = ln(0)/0.05

Since ln(0) is undefined, we need to find the limit as t approaches infinity:

lim t->inf ln(v(t))/t
= lim t->inf [ln(88000) + 0.05t]/t
= 0.05

Therefore, the tree should be harvested at t = 10 years to maximize its value.

If a Tree's Value (V)is Growing According to the Equation v(t)=e.it−.0025stv ( t ) = e ^ { . i t - .0025 s t }v(t)=e.it−.0025st

If a Tree's Value (V)is Growing According to the Equation $v ( t ) = e ^ { . i t - .0025 s t }$