# Question #188b6

##### 1 Answer

#### Explanation:

All you have to do here is to use the following equation

#A_t = A_0 * (1/2)^color(red)(n)#

Here

#A_t# is the mass of the substance thatremains undecayedafter a period of time#t# #A_0# is the initial mass of the substance#color(red)(n)# represents thenumber of half-livesthat pass in a given time period#t#

In your case, you know that the initial mass of the substance is equal to

Now, the number of half-lives that pass in a given time period

#color(red)(n) = t/t_"1/2"#

In your case, the number of half-lives that pass in **years** is equal to

#color(red)(n) = (2100 color(red)(cancel(color(black)("years"))))/(3400color(red)(cancel(color(black)("years")))) = 0.617647#

Plug this into the aforementioned equation and solve for **years**

#A_ "2100 years" = "35 g" * (1/2)^0.617647 = color(darkgreen)(ul(color(black)("23 g")))#

The answer is rounded to two **[sig figs](