Answer :
Given the information on the problem, we can write the following function:
[tex]v(t)=15\cdot(1-0.03)^t[/tex]where v(t) denotes the weight of the element at time t.
Then, to find the time it will take to the element to weight only 3 grams, we have to solve v(t) = 3:
[tex]\begin{gathered} v(t)=3 \\ \Rightarrow15(0.97)^t=3 \\ \Rightarrow(0.97)^t=\frac{3}{15}=\frac{1}{5} \\ \text{Applying natural logarithm on both sides:} \\ \ln (0.97^t)=\ln (0.2) \\ \Rightarrow t\cdot\ln (0.97)=\ln (0.2) \\ \Rightarrow t=\frac{\ln (0.2)}{\ln (0.97)}=52.8\approx53 \end{gathered}[/tex]therefore, it will take approximately 53 years for the element to weight 3 grams