A laboratory stores a sample of the radioactive isotope cesium-137

MATHEMATICS · Multi-part · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A laboratory stores a

150\,\text{mg}

sample of the radioactive isotope cesium-137. The mass

M(t)

, in milligrams, present

t

years after storage satisfies

\dfrac{dM}{dt}=kM

. (a) Calculate the decay constant

k

for cesium-137, given that its half-life is

30.17\,\text{years}

. Express your answer exactly. (b) Determine the least integer number of years required for the mass of the sample to fall below

40\,\text{mg}

. Provide both an exact expression and a decimal approximation correct to the nearest tenth of a year.