# Question #5e9e6

##### 1 Answer

#### Explanation:

Your tool of choice here will be the equation

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

Here

**undecayed** after a period of time

**number of half-lives** that pass in a period of time

In your case, you know that it took **years** for a sample of a given radioactive isotope to decay from *undecayed*.

Your goal here will be to use the above equation to find the value of

#28 color(red)(cancel(color(black)("g"))) = 448 color(red)(cancel(color(black)("g"))) * 1/2^n#

Rearrange to find

#2^n = 448/28 = 16#

Since *power of*

#16 = 2 * 2 * 2 * 2 = 2^4#

you will have

#2^n = 2^4#

This implies that

#n = 4#

So, you know that it takes **years** for **half-lives** to pass, which means that *one half-life*,

#t_"1/2" = "9 years"/4 = color(green)(|bar(ul(color(white)(a/a)color(black)("2.25 years")color(white)(a/a)|)))#