Sales of Version 6.0 of a computer software package start out high and decrease exponentially. At time t, in years, the sales are s (t) = 50e^t dollars per year. After two years, Version 7.0 of the software is released and replaces Version 6.0. Assuming that all income from software sales is immediately invested in government bonds which pay interest at a 6% rate compounded continuously, calculate the total value of sales of Version 6.0 over the two-year period.

Question

Logan Pittman

Business

11 April, 05:21

Sales of Version 6.0 of a computer software package start out high and decrease exponentially. At time t, in years, the sales are s (t) = 50e^t dollars per year. After two years, Version 7.0 of the software is released and replaces Version 6.0. Assuming that all income from software sales is immediately invested in government bonds which pay interest at a 6% rate compounded continuously, calculate the total value of sales of Version 6.0 over the two-year period.

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Penelope Mcmillan · Answer 1

44976 dollars.

Explanation:

At time t, the sale is 50e^ (-t), and there's (2-t) year left to reach the new release of software. During this period, the income after interest is

50e^ (-t) e^ (0.03 (2-t)) = 50e^ (0.06 - 1.03t).

Therefore, the total value of sales is int_0^2 50 e^ (0.06 - 1.03t) dt ~ 44.9758 thousand dollars ~ 44976 dollars.