Asubstance decays according to a = ae-0.057, where i is in hours and ao is the initial amount. determine the half-life of the substance. round your answer to two
decimal places, if necessary.

12.16 hours

Step-by-step explanation:

I'm going to assume my assumption is right.

You can let me know differently.

We want to know the time, t, such that A will be half it's initial population.

This means we want to solve the following equation for t:

Divide both sides by :

Now we are ready to try to get the variable by itself.

Let's rewrite in the equivalent logarithm form:

Divide both sides by -0.057:

Put left hand side into a calculator:

So the half-life is 12.16.  

This means that the initial population will be brought down to half of the initial population in 12.16 hours approximately.