Answer: 24 grams of element would remain.
Step-by-step explanation:
Exponential function for decay:
[tex]f(x)=Ab^{\frac{x}{n}}[/tex] ....(i) , where A = initial value , b = decay factor, x = time , n= time per period
As per given,
A = 569 grams , [tex]b=\dfrac12[/tex]
n= 5 years, t = 23 years
Put all values in (i) , we get
[tex]f(23)=590(\dfrac12)^{\frac{23}{5}}\\\\\\=590\times 0.0412346222117\\\\=24.3284271049\approx 24[/tex]
Hence, after 23 years , 24 grams of element would remain.
