Question

A sample of radioactive isotope of an element contains 60 millions atoms and is found to have a decay rate of 5 hundred atoms per year. What is the half life of the isotope?

Answer 1

Using a linear function, it is found that the half life of the isotope is of 6,000 years.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the quantity and the decay rate, the function for the amount of the isotope is given by:

A(t) = 60,000,000 - 5,000t

The half-life is when the amount is half of the initial amount of 60 millions atoms, hence when A(t) = 30,000,000, so:

30,000,000 = 60,000,000 - 5,000t

5,000t = 30,000,000

t = 30,000,000/5,000

t = 6,000.

More can be learned about linear functions at brainly.com/question/24808124

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