I was running through this mock high school math graduation test (try it out!) http://www.minnpost.com/data/2012/12/can-you-pass-mathematics-grad-test-high-school-students
Question 6 gave me pause:
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year's value. At this rate, what can Dan expect the approximate value of the computer to be after 8 years?
I can solve this easily enough by looping through the calculation for each year's deprecation. Programming has made me lazy, I let loops handle the arithmetic for me. But when solving by hand it was tedious. There must be a better way! Here's what I know: there is a rate of change which is constant at 25% / year, and we know the initial value at $900, and how long the change will be applied, 8 years, but I'm fuzzy on how to put it all together to get a formula.
My college calculus knowledge has imploded on itself, leaving little trace. The Wikipedia page on derivatives is causing my vision to blur. Where do I start to reason my way towards an intelligently-calculated answer?