Question

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x is the number of half-lives that have passed,
(EX. If the half life is 3 days, then 6 days would be 2 half lives and 9 days would be 3 half-lives)
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Question 9 (1 point) ✓ Saved
Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg were
used in a procedure. Write an equation that can be used to determine how much of
the isotope is left after x number of half-lives.
Question 10: how much would be left after 70 days?

Answer 1

The exponential function that is used to determine how much of the isotope is left after x number of half-lives is:

$A(x) = 90(0.5)^x$

5.625 mg would be left after 70 days.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem, considering that it has 90 mg, and the half-life means that r = 0.5, the equation is:

$A(x) = A(0)(1 - r)^x$

$A(x) = 90(0.5)^x$

70 days is 70/17.5 = 4 half-lifes, hence:

$A(4) = 90(0.5)^4 = 5.625$

5.625 mg would be left after 70 days.

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