The curve given by and is defined for all real

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The curve given by

x=e^{2t}

and

y=e^{t}

is defined for all real

t

. Which statement describes the behavior of the slope

\dfrac{dy}{dx}

t

increases? (a) It is positive for all

t

and increases as

t

increases. (b) It is positive for all

t

and decreases as

t

increases. (c) It is positive and constant for all

t

. (d) It equals zero when

t=0