Choose the one alternative that best completes the statement or answers the question.
-In the formula $\mathrm { A } ( \mathrm { t } ) = \mathrm { A } _ { 0 } \mathrm { e } ^ { \mathrm { kt } } , \mathrm { A }$ is the amount of radioactive material remaining from an initial amount $\mathrm { A } _ { 0 }$ at a given time $\mathrm { t }$, and $\mathrm { k }$ is a negative constant determined by the nature of the material A certain radioactive isotope decays at a rate of $0.25 \%$ annually. Determine the half-life of this isotope, to the nearest year.
A) $3 \mathrm { yr }$
B) $277 \mathrm { yr }$
C) $120 \mathrm { yr }$
D) $200 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope is found by setting $A = \frac{1}{2}A_0$ and solving for $t$. Given the decay rate of $0.25\%$, $k = -0.0025$. Substituting these values into the formula and solving for $t$ gives a half-life of approximately $277$ years.

Choose the One Alternative That Best Completes the Statement or Answers