Solve the problem.
-The half-life of a certain radioactive substance is 22 years. Suppose that at time $t = 0$, there are $24 \mathrm {~g}$ of the substance. Then after t years, the number of grams of the substance remaining will be:
$N ( t ) = 24 \left( \frac { 1 } { 2 } \right) ^ { t / 44 }$
How many grams of the substance will remain after 242 years? Round to the nearest hundredth when necessary.
A) $0.53 \mathrm {~g}$
B) $0.07 \mathrm {~g}$
C) $0.27 \mathrm {~g}$
D) $0.13 \mathrm {~g}$

Question

Quizplus · Accepted Answer

The half-life of the substance is 22 years, so after 242 years, the substance will have gone through 242/22 = 11 half-lives. Each half-life reduces the amount of substance by half, so after 11 half-lives, only 1/2^11 = 0.000488 of the original amount will remain. Therefore, after 242 years, there will be 24 * 0.000488 = 0.0117 grams of the substance remaining, which rounds to 0.01 grams.

Solve the Problem t=0t = 0t=0 , There Are 24 g24 \mathrm {~g}24 g

Solve the Problem $t = 0$ , There Are $24 \mathrm {~g}$