Question

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)`. What is the half life of the substance?

Answer 1

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=0`:
`A_0 = 346 (1/2)^(0/15) = 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) = 1/2`
So obviously
`T_(half) / 15 = 1 implies T_(half) = 15`

So the half life is 15 days.