(a) State the nature of the graph of with respect to monotonicity for (i) , and (ii)…

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

Problem

(a) State the nature of the graph of

y=a^{x}

with respect to monotonicity for (i)

a>1

, and (ii)

0<a<1

. (b) An exponential curve passes through the point

(0,1)

and is observed to fall as

x

increases. Without performing any numerical calculation, decide whether its base lies in the interval

0<a<1

or satisfies

a>1

. Give a brief reason. (c) Describe qualitatively how the initial steepness of the curve at

(0,1)

changes when the value of the base

a

is gradually increased from just above

0

to very large values.