The quantity satisfies with initial amount

MATHEMATICS · Single correct · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

The quantity

Q

satisfies

\dfrac{dQ}{dt}=kQ

with initial amount

Q_0

. Which of the following expressions gives the time

t

required for the quantity to reach

5Q_0

? (a)

t=\dfrac{5}{k}

(b)

t=\dfrac{\ln 5}{k}

(c)

t=k\,\ln 5

(d)

t=\ln(5k)