Write the word or phrase that best completes each 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 $t$, and $\mathrm { k }$ is a negative constant determined by the nature of the material A certain radioactive isotope decays at a rate of $0.225 \%$ annually. Determine half-life of this isotope, to the nearest year.
A) $308 \mathrm { yr }$
B) $134 \mathrm { yr }$
C) $222 \mathrm { yr }$
D) $3 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope is found by setting $A(t) = \frac{1}{2}A_0$ and solving for $t$. Given the decay rate of $0.225\%$, $k = -0.00225$. Using the formula $t = \frac{\ln(1/2)}{k}$, we find $t \approx 308$ years.

Write the Word or Phrase That Best Completes Each Statement A(t)=A0ekt,A\mathrm { A } ( \mathrm { t } ) = \mathrm { A } _ { 0 } \mathrm { e } ^ { \mathrm { kt } } , \mathrm { A }A(t)=A0​ekt,A

Write the Word or Phrase That Best Completes Each Statement $\mathrm { A } ( \mathrm { t } ) = \mathrm { A } _ { 0 } \mathrm { e } ^ { \mathrm { kt } } , \mathrm { A }$