# Calculus

A certain radioactive material decays exponetially. The percent, P, of the material left after t years is given by P(t)= 100(1.2)^-t
a)Determine the half life of the substance

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1. From the equation we can see that the original amount was 100 units
So we want to know when that amount becomes 50
50 = 100(1.2)^-t
.5 = 1.2^-t
log(.5)= log(1.2^-t)
log(.5)= -tlog(1.2)
-t = log(.5)/log(1.2)
= -3.8

so t = 3.8 years is the half-life time

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