A radioactive substance obeys

CHEMISTRY · Single correct · ISC · Mathematics · Calculus · Continuity

Problem

\dfrac{dM}{dt}=k(t)M

, where

k(t)=-0.04

for

0\le t<10

and

k(t)=-0.02

for

t\ge10

, with

t

measured in years. Which statement about the mass

M(t)

t=10

is necessarily true? (a) Both

M

and

\dfrac{dM}{dt}

are continuous at

t=10

. (b)

M

is continuous at

t=10

, while

\dfrac{dM}{dt}

has a jump discontinuity there. (c)

M

is continuous at

t=10

, but it is not differentiable there, so

\dfrac{dM}{dt}

does not exist at

t=10

. (d)

M

has a jump discontinuity at

t=10

, but

\dfrac{dM}{dt}

is continuous there.