Sales of the text "Calculus and You" have been declining continuously at an annual rate of 8%. Assuming that "Calculus and You" currently sell 800 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. Use the formula for continuously compounded interest with a negative rate.
A)100,000 copies
B) 80,000 copies
C) 10,000 copies
D) 250,000 copies
E) 500,000 copies

Question

Sales of the text "Calculus and You" have been declining continuously at an annual rate of 8%. Assuming that "Calculus and You" currently sell 800 copies per year and that sales will continue this pattern of decline, calculate total future sales of the text. Use the formula for continuously compounded interest with a negative rate. ​
A)100,000 copies
B) 80,000 copies
C) 10,000 copies
D) 250,000 copies
E) 500,000 copies

Quizplus · Accepted Answer

The formula for continuously compounded interest is A = P * e^(rt). Here, P = 800, r = -0.08, and t approaches infinity. The total future sales can be calculated as the integral of 800 * e^(-0.08t) from 0 to infinity, which equals 10,000 copies.

Sales of the Text "Calculus and You" Have Been Declining