This is a free lesson from our course in Amsco's Integrated Algebra

In this lesson you’ll learn about the Graphs Involving Exponential Functions
and how to draw the graphs involving exponential function. Before starting this lesson,
you may recall
earlier learning with exponents. What is different here is that variable
x is now exponent, where before, the variable x was in the base. The function f
defined by f (x) = a ^{x}, where a > 0, a
¹1, and the exponent x is any
real number, is called an exponential function.
Note: the variable x is in the exponent as opposed to the base, in case of exponential
functions. Also the base a is restricted to being a positive number other than 1.
(More text below video...)

(Continued from above)
Further on you’ll learn how to graph exponential functions. The major steps are
as given below:
• find ordered pairs i.e. put in the same values for x each time and then find the
corresponding y value for the function you are working at.
• plot the points – the process is same way like when graph the lines
• draw the curve – the representative curve(s) of an exponential function will look
like the following:

For example: Given- Graph the exponential function f(x) = 4 x
It may be noted that here base is 4 and the exponent is variable x.
• the ordered pairs are as below:

• plot the points and draw curve: the curve looks like,

There on you’ll learn the concepts of exponential growth over an interval like-
populations of bacteria, people, compound interest etc., who grow exponentially
AND exponential decay like- a decrease in population, a fund, or the radioactive
decay of an element such as carbon etc. Note that in exponential decay, the rate
of change is a negative.
For example: Given- The population of a town is decreasing at the rate of 2.5%/
year. If the population in the year 2010 was 28,000, what will be the expected population
in 2025, if it decrease at this rate? You can solve this, using the formula for
exponential decay, where r = 0.025, Jis the initial population and n = 15 years.
So, A = J(1 + r)^{n} = 28,000 [1 + (–0.025)) ] ^{15} = 28,000(0.975)
^{15} = 19,152.5792.
The population will be about 19,000 in 2025, as the final answer.
The video above explains more details on Graphs involving exponential functions
and application of real world problems, with the help of several examples and their
solutions.

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