radium-226, a common isotope of radium, has a half - life of 1,620 years. the following half - life model…

radium-226, a common isotope of radium, has a half - life of 1,620 years. the following half - life model shows how much of a 120 - gram sample of radium-226 will remain after t years. $p(t)=120(\frac{1}{2})^{\frac{t}{1620}}$. after 100 years, about grams of the sample will remain. 60 100 115

radium-226, a common isotope of radium, has a half - life of 1,620 years. the following half - life model shows how much of a 120 - gram sample of radium-226 will remain after t years. $p(t)=120(\frac{1}{2})^{\frac{t}{1620}}$. after 100 years, about grams of the sample will remain. 60 100 115

Answer

Explanation:

Step1: Substitute $t = 100$ into formula

$P(100)=120(\frac{1}{2})^{\frac{100}{1620}}$

Step2: Simplify the exponent

$\frac{100}{1620}=\frac{5}{81}$ So $P(100)=120(\frac{1}{2})^{\frac{5}{81}}$

Step3: Calculate the value

$(\frac{1}{2})^{\frac{5}{81}}\approx0.96$ $P(100)=120\times0.96 = 115.2\approx115$

Answer:

115