For the function with

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

For the function

y=Ce^{kt}

with

C>0

, which statement best describes the relationship between the doubling time

T_{2}

and the sign of

k

? (a)

T_{2}

equals

\dfrac{\ln 2}{|k|}

, so it is positive for both

k>0

and

k<0

. (b)

T_{2}

is defined and positive only when

k>0

; if

k<0

, a doubling time does not exist. (c) Because

T_{2}=\dfrac{\ln 2}{k}

, it is negative whenever

k>0

and positive whenever

k<0

. (d)

T_{2}

is defined and positive only when

k<0

; if

k>0

, a doubling time does not exist.