Derek S. answered • 04/25/15
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If the computer loses half its value every year, then you can write the equation as 1600 * (1/2)^t, where 1600 is the original value of the computer, and (1/2)^t multiplies the original value times 1/2 for every year, which is represented as t.
To solve for 1600 * (1/2)^t = 250, we can divide both sides by 1600 to get: (1/2)^t = 250/1600 = 5/32.
Next, what you want to do is take the log of both sides, and use log rules to get the t out by itself (Hint: log [a^-x] = -x log [a]).
All that's left after that point is simplification or just plugging it into a calculator. If you simplify it, your final answer should consist of log[2] and log[5] expressions. Either way, t should fall somewhere between 2.5 and 2.8.
To solve for 1600 * (1/2)^t = 250, we can divide both sides by 1600 to get: (1/2)^t = 250/1600 = 5/32.
Next, what you want to do is take the log of both sides, and use log rules to get the t out by itself (Hint: log [a^-x] = -x log [a]).
All that's left after that point is simplification or just plugging it into a calculator. If you simplify it, your final answer should consist of log[2] and log[5] expressions. Either way, t should fall somewhere between 2.5 and 2.8.
