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Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 450,000 tritium atoms remained undisturbed for 11 years. How much tritium does the bottle contain now?
If necessary, round your answer to the nearest whole number

Respuesta :

Using an exponential function, it is found that the bottle contains 255,960 atoms of tritium after 11 years.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • The bottle initially contained 450,000 tritium atoms, hence A(0) = 450000.
  • The amount decays by about 5% per year, hence r = 0.05.

Thus, the equation is given by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 450000(1 - 0.05)^t[/tex]

[tex]A(t) = 450000(0.95)^t[/tex]

After 11 years, the amount is given by:

[tex]A(11) = 450000(0.95)^{11} = 255960[/tex]

The bottle contains 255,960 atoms of tritium after 11 years.

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

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