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A sample of a radioactive isotope had an initial mass of 480 mg in the year 2009 and decays exponentially over time. A measurement in the year 2011 found that the sample's mass had decayed to 390 mg. What would be the expected mass of the sample in the year 2016, to the nearest whole number?

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Trancescient

Answer:

A = 232 mg

Step-by-step explanation:

First, we need to find the half-life (hl) of the isotope:

A = A02^-(t/hl) taking the natural logarithm of both sides

ln(A/A0) = -(t/hl)ln2 or

hl = -t ln2 /ln(A/A0)

= -(2 yrs)ln2 / ln(390/480)

= 6.68 yes

After 7 years, in 2016 we expect the mass of the isotope to be

A = (480mg)2^-(7/6.68)

= 232 mg

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