The exponential function that can be used to determine how much of the isotope is left after x number of half-lives is given by:
[tex]A(x) = 90(0.5)^x[/tex]
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 initial amount is of A(0) = 90 mg, and we are working with half-lifes, hence r = 0.5, which means that the equation is:
[tex]A(x) = 90(0.5)^x[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
