(a) State the monotonicity property of the exponential function separately for the…

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

(a) State the monotonicity property of the exponential function

y=a^{x}

separately for the cases (i)

a>1

and (ii)

0<a<1

. (b) Prove that if

0<a<1

and

x<y

, then

a^{x}>a^{y}

. (c) Using the result obtained in part (b), determine which of the two numbers

(\tfrac12)^{\sqrt3}

and

(\tfrac12)^{\pi}

is greater, clearly justifying your answer.