For a quantity that changes according to with initial condition

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

For a quantity that changes according to

\dfrac{dy}{dt}=ky

with initial condition

y(0)=y_0

, which of the following expresses the relationship between

y

and

t

as a linear equation in

t

? (a)

y= y_0 + kt

(b)

\ln y = y_0 + kt

(c)

\ln y = \ln y_0 + kt

(d)

y = y_0 e^{kt}