A radioactive sample obeys for

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A radioactive sample obeys

\frac{dM}{dt}=-0.05M

for

0\le t\le 4\,\text{days}

. At

t=4\,\text{days}

, new shielding is added and for

t>4\,\text{days}

the decay law becomes

\frac{dM}{dt}=kM

, where

k

is constant. Given

M(0)=50\,\text{g}

and

M(10)=20\,\text{g}

, determine the value of

k

(include units).