For an exponential model that satisfies and with

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

For an exponential model

y=y_0e^{kt}

that satisfies

y(0)=y_0

and

y(t_1)=y_1

with

y_1>0

, which of the following expressions gives the value of

k

in terms of

y_0,\,y_1,

and

t_1

? (a)

k=\dfrac{\dfrac{y_1}{y_0}}{t_1}

(b)

k=\dfrac{y_1-y_0}{y_0 t_1}

(c)

k=\dfrac{\ln\left(\dfrac{y_1}{y_0}\right)}{t_1}

(d)

k=\dfrac{\ln\left(\dfrac{y_0}{y_1}\right)}{t_1}