Question

radium - 226, a common isotope of radium, has a half - life of 1,620 years. how many grams of a 120 - gram sample will remain after t years? which equation can you use to solve this problem? 226 = 120(\frac{1}{2})^{\frac{t}{1620}} p(t)=120(\frac{1}{2})^{\frac{t}{1620}} 120=(\frac{1}{2})^{\frac{t}{1620}} p(t)=\frac{1}{2}(120)^{\frac{1}{1620}}

Explanation:

Step1: Recall half - life formula

The general formula for radioactive decay is $P(t)=P_0(\frac{1}{2})^{\frac{t}{h}}$, where $P_0$ is the initial amount, $t$ is the time elapsed, and $h$ is the half - life.

Step2: Identify values

Here, $P_0 = 120$ grams (initial sample size), $h = 1620$ years (half - life), and we want to find the amount $P(t)$ after $t$ years.

Answer:

$P(t)=120(\frac{1}{2})^{\frac{t}{1620}}$