radium - 226, a common isotope of radium, has a half - life of 1,620 years. how many grams of a 120 - gram…

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}} 120=(\\frac{1}{2})^{\\frac{t}{1620}} p(t)=120(\\frac{1}{2})^{\\frac{t}{1620}} done

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}} 120=(\\frac{1}{2})^{\\frac{t}{1620}} p(t)=120(\\frac{1}{2})^{\\frac{t}{1620}} done

Answer

Answer:

C. $P(t)=120\left(\frac{1}{2}\right)^{\frac{t}{1620}}$

Explanation:

Step1: Recall half - life formula

The general formula for exponential decay with half - life is $P(t)=P_0\left(\frac{1}{2}\right)^{\frac{t}{h}}$, 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).

Step3: Substitute values

Substituting into the formula gives $P(t)=120\left(\frac{1}{2}\right)^{\frac{t}{1620}}$.