How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the functi $\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - 0.189 t }$ , where t is the time in years? Round your answer to the nearest
Hundredth year.
A) 3.67 years
B) 34.27 years
C) 122.85 years
D) 37.94 years

Question

Quizplus · Accepted Answer

To find the half-life, set $A(t) = \frac{650}{2}$ and solve for $t$. This gives $325 = 650e^{-0.189t}$. Dividing both sides by 650 and taking the natural logarithm leads to $-0.189t = \ln(0.5)$, and solving for $t$ gives $t \approx 3.67$ years.

How Long Will It Take a Sample of Radioactive Substance A(t)=650e−0.189t\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - 0.189 t }A(t)=650e−0.189t

How Long Will It Take a Sample of Radioactive Substance $\mathrm { A } ( \mathrm { t } ) = 650 \mathrm { e } ^ { - 0.189 t }$