Suppose you are given a radioactive substance. After 30 days there is 1/10 of the original
amount remaining. What is the half life of the substance? (Your answer may include
logs)

Question

anonymous · Answer

I used to know how to do this but I've since forgotten (and it may be on my final tomorrow). Is the equation: $$P(t) = P _{0}e ^{kt}$$ ?

anonymous · Answer

-kt

anonymous · Answer

Close! 

$$P(t) = P_0e ^{-kt}$$

The exponent of Euler's number must be negative because as time increases, the amount remaining must progressively become a smaller fraction of the initial amount.

anonymous · Answer

Ah, got it. Thanks. For an increasing function (after 10 days the population doubles), it would be positive kt, right?