Question

Each week ab album sells 4% fewer copies than it did the previous week. this week it sold 12400 copies. at this rate in how many weeks will it sell fewer than 2000 copies

Answer 1

It will be 45 weeks until the album sells fewer than 2000 copies. We can look at the equation (0.96)^x = 2000/12400 to find the number of weeks, x, that the 4 percent reduction will yield the ratio of sales endpoint to sales now. We can solve the equation by taking a log of both sides in order to isolate the x variable. Using the natural log, we'd have x*ln(0.96) = ln(2000/12400). Solving this shows x to be ~=44.69525, so we round up to 45 weeks. We can confirm our solution by verifying that 0.96^45 is indeed less than 2000/12400. (0.159.. < 0.161...)