A certain radioactive isotope has a half-life of 37 years. How many years will it take for 100 grams to decay to 64 grams?
A) 18.17 years
B) 33.54 years
C) 23.82 years
D) 28.71 years
E) 24.89 years

Question

Quizplus · Accepted Answer

The decay of a radioactive isotope follows an exponential decay model, where the amount remaining after a certain time can be calculated using the formula $A = P(1/2)^{t/T}$, where $A$ is the amount remaining, $P$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life of the substance. Here, we want to find $t$ when $P = 100$ grams, $A = 64$ grams, and $T = 37$ years. Rearranging the formula to solve for $t$, we get $t = T \log_2(P/A)$. Substituting the given values, $t = 37 \log_2(100/64)$, which calculates to approximately 23.82 years.

A Certain Radioactive Isotope Has a Half-Life of 37 Years