Respuesta :
Answer: A=100(12)t5.27
Step-by-step explanation:
Assume / and ^ got lost from eqns.
A(t) = initial × (1/2)^(t/halflife)
So initial = 100, halflife = 5.27,
A=100(12)t5.27 means A=100(1/2)^(t/5.27)
so that A is 50 when t is 5.27
The equation that determines the percent of an initial amount of the isotope in time is [tex]a = 100\cdot \left(\frac{1}{2}\right)^{\frac{t}{5.27} }[/tex]. (Correct choice: C)
Procedure - Determination of the decay model for a radioisotope
The mass of the radioisotope ([tex]m(t)[/tex]), in miligrams, decays exponentially in time ([tex]t[/tex]), in years, whose behavior in terms of its half-life ([tex]t_{1/2}[/tex]), in years, is described below:
[tex]m(t) = m_{o}\cdot \left(\frac{1}{2} \right)^{\frac{t}{t_{1/2}} }[/tex] (1)
Where [tex]m_{o}[/tex] is the initial mass of the radioisotope, in miligrams.
And the percentage of an initial mass of the radioisotope remaining is:
[tex]a = 100\cdot \left(\frac{1}{2} \right)^{\frac{t}{t_{1/2}} }[/tex]
If we know that [tex]t_{1/2} = 5.27\,yr[/tex], then the equation is:
[tex]a = 100\cdot \left(\frac{1}{2}\right)^{\frac{t}{5.27} }[/tex]
The equation that determines the percent of an initial amount of the isotope in time is [tex]a = 100\cdot \left(\frac{1}{2}\right)^{\frac{t}{5.27} }[/tex]. (Correct choice: C) [tex]\blacksquare[/tex]
Remark
The statement presents mistakes, correct form is shown below:
The radioisotope Cobalt-60 is used in cancer therapy. The half-life of this isotope is 5.27 years. Which equation determines the percent of an initial amount of the isotope remaining after [tex]t[/tex] years?
A) [tex]a = 100\cdot \left(\frac{1}{12}\right)^{\frac{5.27}{t} }[/tex]
B) [tex]a = 5.27\cdot \left(\frac{1}{2} \right)^{\frac{100}{t} }[/tex]
C) [tex]a = 100\cdot \left(\frac{1}{12} \right)^{\frac{t}{5.27} }[/tex]
D) [tex]a = 5.27\cdot \left(\frac{1}{2} \right)^{\frac{t}{100} }[/tex]
To learn more on isotopes, we kindly invite to check this verified question: https://brainly.com/question/13214440
