EXPONENTIAL FUNCTIONS AND
EQUATIONS
Tutorial Manual
MUT
Maths 2
, Intended Learning Outcomes
When you have finished this handout and done the learning activities, you should
be able to
Apply the knowledge of quadratic equations to solve exponential equations
Introduction
In this handout, we go over exponential functions and equations of base e. In
particular, we want to be able to apply the knowledge of quadratic equations to
solve exponential equations without the use of a calculator. Understanding of the
graphs of exponential logarithmic functions and their domains and ranges is
necessary to solve such equations completely as some of the solutions you get are
not feasible and must be discarded. The main purpose of this guide is to serve as
a gentle introduction to the next handout on Hyperbolic functions.
Exponential Functions
An exponential function is a function which has the unknown in the power. The
general formula of an exponential function is
f x ab x
a 0, b 0, b 1
The value b is the base of the exponential. Base 10 is a common base given that
counting is introduced in this base. Other important bases are base 2 which is
important in Computer Science and base e , called the natural base, which is of
particular importance in engineering and natural sciences. e is an irrational
number which has a value of e 2.718281828...
From the natural base e , we have the natural exponential function which is given
by
f x ex
1
EQUATIONS
Tutorial Manual
MUT
Maths 2
, Intended Learning Outcomes
When you have finished this handout and done the learning activities, you should
be able to
Apply the knowledge of quadratic equations to solve exponential equations
Introduction
In this handout, we go over exponential functions and equations of base e. In
particular, we want to be able to apply the knowledge of quadratic equations to
solve exponential equations without the use of a calculator. Understanding of the
graphs of exponential logarithmic functions and their domains and ranges is
necessary to solve such equations completely as some of the solutions you get are
not feasible and must be discarded. The main purpose of this guide is to serve as
a gentle introduction to the next handout on Hyperbolic functions.
Exponential Functions
An exponential function is a function which has the unknown in the power. The
general formula of an exponential function is
f x ab x
a 0, b 0, b 1
The value b is the base of the exponential. Base 10 is a common base given that
counting is introduced in this base. Other important bases are base 2 which is
important in Computer Science and base e , called the natural base, which is of
particular importance in engineering and natural sciences. e is an irrational
number which has a value of e 2.718281828...
From the natural base e , we have the natural exponential function which is given
by
f x ex
1
