# Calculus

posted by lala

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

1. Reiny

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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