Model Exponential Growth and Decay
Solve.
-The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? (Round your answer to three decimal places.)
A)22.383
B)29.134
C)1.604
D)0

Question

Quizplus · Accepted Answer

The amount of silicon-32 remaining after 300 years can be calculated using the formula for exponential decay, $A = P(1/2)^{t/T}$, where $A$ is the amount remaining, $P$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Substituting $P = 30$ grams, $t = 300$ years, and $T = 710$ years, we get $A = 30(1/2)^{300/710}$, which rounds to approximately 22.383 grams.