Solution: This is an exponential decay problem, so we know that the formula is of the type P(t) = P0 at. We know that when we plug in t=100 we get 0.5*P0. We also know from the formula that P(100) = P0a100. Setting these two equal to each other and solving for a, we get a = (1/2)100, and the formula becomes P(t) = P0(1/2) t/100. We now want to know when P(t) = P0(1/2)t/100 = 0.1*P0; using logs to solve for t, we get t = 100log(0.1)/log(1/2).

Next Problem