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Radioactive isotope Carbon-14 decays at a rate proportional to the amount present. If the decay rate is 12.10% per thousand years and the current mass is 135.2 mg, what will the mass be 2.2 thousand years from now?

Respuesta :

Using an exponential function, it is found that the mass 2.2 thousand years from now will be of 103.6 mg.

What is an exponential function?

It is modeled by:

[tex]A(t) = A(0)e^{-k\frac{t}{n}}[/tex]

In which:

  • A(0) is the initial value.
  • k is the decay rate per n years.

In this problem:

  • The decay rate is 12.10% per thousand years, hence k = 0.121, n = 1000.
  • The current mass is 135.2 mg, hence A(0) = 135.2.

Then:

[tex]A(t) = A(0)e^{-k\frac{t}{n}}[/tex]

[tex]A(t) = 135.2e^{-0.121\frac{t}{1000}}[/tex]

The mass 2.2 thousand years from now will be given by:

[tex]A(2200) = 135.2e^{-0.121\frac{2200}{1000}} = 103.6[/tex]

The mass 2.2 thousand years from now will be of 103.6 mg.

More can be learned about exponential functions at https://brainly.com/question/25537936

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