(a) Define an exponential function and distinguish between the terms "exponential…

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

1. (a) Define an exponential function and distinguish between the terms "exponential growth" and "exponential decay" in the context of its graph. (b) For the functions

f(x)=1.5^{x}

and

g(x)=\left(\dfrac1{1.5}\right)^{x}

, state in each case: (i) whether the curve is increasing or decreasing, (ii) the horizontal asymptote, (iii)

\displaystyle\lim_{x\to\infty}f(x)

and

\displaystyle\lim_{x\to\infty}g(x)

. Give reasons for each answer. (c) Explain why the point

(0,1)

always lies on the graph of

y=a^{x}

for any valid base

a

. (d) Describe, without calculation, how the graphs of

f

and

g

are related to each other geometrically.

Related theory

Growth Models
Exponential Functions
Exponential and Logarithmic Functions
Functions

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