AP Calculus ABhardmcq1 pt

A radioactive substance decays at a rate proportional to the amount present, losing 2%2\% of its mass per year. If the initial mass is 100100 grams, when will the mass reach 5050 grams?

A.ln20.02\dfrac{\ln 2}{0.02} years
B.5050 years
C.ln22\dfrac{\ln 2}{2} years
D.0.02ln2\dfrac{0.02}{\ln 2} years

Explanation

Core Concept

The model is m(t)=100e0.02tm(t) = 100e^{-0.02t}, and setting 50=100e0.02t50 = 100e^{-0.02t} gives t=ln20.0234.7t = \dfrac{\ln 2}{0.02} \approx 34.7 years.

Correct Answer

Aln20.02\dfrac{\ln 2}{0.02} years

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