Question

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

Answer 1

Answer: 24 grams of element would remain.

Step-by-step explanation:

Exponential function for decay:

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

As per given,

A = 569 grams , $b=\dfrac12$

n= 5 years, t = 23 years

Put all values in (i) , we get

$f(23)=590(\dfrac12)^{\frac{23}{5}}\\\\\\=590\times 0.0412346222117\\\\=24.3284271049\approx 24$

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