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

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...)

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