# A research assistant made 160 mg of radioactive sodium (Na^24) and found that there was only 20 mg left 45 h later, how much of the original 20 mg would be left in 12 h?

##### 2 Answers

#### Explanation:

Let rate of decay be

So we can write

or

or

or

or

Similarly after

Just to use the conventional radioactive decay model as a slight alternative method.

After 12hr we have 11.49mg

#### Explanation:

Let

It's a fairly simple model to solve with ODEs but as it's not really related to the question, we end up with

First we find the value of

Take natural logs of both sides:

So starting with