Final answer:
The value of sales of Version 3.0 over the three year period can be calculated by integrating the sales function from 0 to 3 years and then applying the future value formula with continuous compounding at 5% interest rate.
Step-by-step explanation:
The student is asking about calculating the total value of sales of a software product over a period of three years, considering the sales decrease exponentially and the proceeds are invested at a continuous compound interest rate. To determine this, we integrate the sales function to find the total sales over the three years and then calculate the future value of these sales at 5% interest compounded continuously.
Steps to Calculate Total Value of Sales
Integrate the sales function s(t) = 50e−t from t = 0 to t = 3 to find the total sales in thousands of dollars.
Apply the continuous compound interest formula to the result of the integration to find the future value.
Integration of Sales Function
The indefinite integral of s(t) is −50e−t+ C. Evaluating from 0 to 3, we get:
Total Sales = (-50e−3 + 50) - (-50 + 50) = 50 - 50e−3.
Calculating Future Value
We use the formula Future Value = Present Value * e(Interest Rate * Time).
Since the interest is compounded continuously, we calculate the future value of the total sales over the three years using the interest rate of 5%:
Future Value = (50 - 50e−3) * e(0.05 * 3).