Exponential functions... Can someone help me solve this?

A radioactive substance decays so much that the amount present t days from now is 346(1/2) ^(t/15)346(12)t15. What is the half life of the substance?

1 Answer
Apr 29, 2018

15 days

Explanation:

The half life is the point where we have 1/2 of the substance left from the beginning.

So what do we have at the beginning? Let's plug in t=0t=0:
A_0 = 346 (1/2)^(0/15) = 346 A0=346(12)015=346

Now, we want something to be half of that, so let's set the amount equal to half of 346:
A = 1/2 * 346 = 346 * (1/2)^(T_(half) / 15) implies (1/2)^(T_(half}/15) = 1/2A=12346=346(12)Thalf15(12)Thalf15=12
So obviously
T_(half) / 15 = 1 implies T_(half) = 15 Thalf15=1Thalf=15

So the half life is 15 days.