Write the word or phrase that best completes each statement or answers the question.
-How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function $\mathrm { A } ( \mathrm { t } ) = 450 \mathrm { e } ^ { - .168 \mathrm { t } }$, where $\mathrm { t }$ is the time in years? Round your answer to the nearest hundredth year.
A) $4.13 \mathrm { yr }$
B) $36.36 \mathrm { yr }$
C) $75.60 \mathrm { yr }$
D) $40.49 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the half-life, set $A(t) = \frac{450}{2}$ and solve for $t$. The equation becomes $225 = 450e^{-0.168t}$. Dividing both sides by 450 gives $0.5 = e^{-0.168t}$. Taking the natural logarithm of both sides gives $\ln(0.5) = -0.168t$. Solving for $t$ gives $t = \frac{\ln(0.5)}{-0.168} \approx 4.13$ years.

Write the Word or Phrase That Best Completes Each Statement A(t)=450e−.168t\mathrm { A } ( \mathrm { t } ) = 450 \mathrm { e } ^ { - .168 \mathrm { t } }A(t)=450e−.168t

Write the Word or Phrase That Best Completes Each Statement $\mathrm { A } ( \mathrm { t } ) = 450 \mathrm { e } ^ { - .168 \mathrm { t } }$