High School

Solve the formula for the half-life of a radioactive isotope given:

[tex]A_2 = \frac{A_1}{2^n}[/tex]

where [tex]A_1 = 3700[/tex] and [tex]A_2 = 200[/tex].

Find the value of [tex]n[/tex].

Answer :

Final answer:

The formula for the half-life of a radioactive isotope is n = log(A1/A2) / log(r), where A1 is the initial amount, A2 is the final amount, and r is the decay constant. However, to determine the value of n, we need to know the value of the decay constant as well.

Explanation:

The formula for the half-life of a radioactive isotope is given by:

n = logA1/A2 / logr

where A1 is the initial amount, A2 is the final amount, and r is the decay constant.

Plugging in the given values, we have n = log3700/200 / logr. However, in order to find the value of n, we also need the value of the decay constant (r). Without that information, we cannot determine the value of n.

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