Question

Suppose that the function V(t)=2+4t approximates the volume of timber in a forest at a period of time (t) What is the change the volume of time at time period 10? Answer: Suppose that the function V(t)=2+4t approximates the volume of timber in a forest at a period of time (t). What is the percentage change in the volume of time at time period 10? (Round to the nearest two decimal places. Do not include a % sign in your response.) Answer: Suppose that the function V(t)=2+4t approximates the volume of timber in a forest at a period of time (t). The percentage change in volume formula is given by g(t)=4/(2+4t). If the forester has a single-rotation harvest, determine the optimal time until harvest (t) when the interest rate is 12.59 Answer: Suppose that the function V(t)=2+4t approximates the volume of timber in a forest at a period of time (t). The percentage change in volume formula is given by g(t)=4/(2+4t). If the forester has a single-rotation harvest, determine the optimal time until harvest (t) when the interest rate falls to 103 s Answer:

Answer 1

Answer:Therefore, the optimal time until harvest is 9.8 years.

Explanation:

The function V(t)=2+4t approximates the volume of timber in a forest at a period of time (t). The change in the volume of timber at time period 10 is calculated as follows:

V(10) = 2 + 4 * 10 = 42

The percentage change in the volume of timber at time period 10 is calculated as follows:

g(10) = 4 / (2 + 4 * 10) = 0.0909

To the nearest two decimal places, the percentage change in the volume of timber at time period 10 is 0.09.

The optimal time until harvest (t) when the interest rate is 12.59 is calculated as follows:

g(t) = 12.59

4 / (2 + 4t) = 12.59

2 + 4t = 32

4t = 30

t = 7.5

Therefore, the optimal time until harvest is 7.5 years.

The optimal time until harvest (t) when the interest rate falls to 10.3 is calculated as follows:

g(t) = 10.3

4 / (2 + 4t) = 10.3

2 + 4t = 41.2

4t = 39.2

t = 9.8