# Question #e2e73

##### 1 Answer

#### Answer:

#### Explanation:

The idea here is that you need to find the amount of *phosphorus-32* that will decay in **five days** to leave behind

Notice that problem provides you with the isotope's **nuclear half-life**, which as you know tells you how much time is needed for a sample of radioactive substance to decay to **half** of its *initial value*.

If you take

#color(blue)(|bar(ul(color(white)(a/a)A = A_0 * 1/2^n color(white)(a/a)|)))#

Here **number of half-lives** that pass in a given amount of time and is calculated using

#color(blue)(|bar(ul(color(white)(a/a)n = "period of time"/"half-life"color(white)(a/a)|)))#

You know that the sample must travel for **days**, and that phosphorus-32 has a half-life of **days**, which means that

#n = (5 color(red)(cancel(color(black)("days"))))/(14.3color(red)(cancel(color(black)("days")))) = 0.34965035#

Rearrange the first equation to solve for

#A = A_0 * 1/2^n implies A_0 = A * 2^n#

Plug in your values to find

#A_0 = "0.15 Ci" * 2^0.34965035 = color(green)(|bar(ul(color(white)(a/a)"0.19 Ci"color(white)(a/a)|)))#

I'll leave the answer rounded to two **sig figs**.