Question

Element X is a radioactive isotope such that every 5 years, its mass decreases by half.

Given that the initial mass of a sample of Element X is 590 grams, how much of the
element would remain after 23 years, to the nearest whole number?

Answer 1

Answer: 24 grams of element would remain.

Explanation:

Exponential function for decay:

`f(x)=Ab^{(x)/(n)}` ....(i) , where A = initial value , b = decay factor, x = time , n= time per period

As per given,

A = 569 grams ,
`b=\frac12`

n= 5 years, t = 23 years

Put all values in (i) , we get

`f(23)=590(\frac12)^{(23)/(5)}\\\\\\=590* 0.0412346222117\\\\=24.3284271049\approx 24`

Hence, after 23 years , 24 grams of element would remain.