A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function S(t)=46+12e^−0.04t, where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first six years.

The average price of the stock over the first six years is 56.669 US dollars.

Step-by-step explanation:

Since the price is a continuous and differentiable function, we can determine the average price by means of the following integral equation:

(1)

Where:

- Initial time, measured in years.

- Final time, measured in years.

If we know that , and , then the average price of the stock over the first six years is:

(2)

The average price of the stock over the first six years is 56.669 US dollars.

step-by-step explanation:

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743