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 Amsco Integrated Algebra I: Graphs Involving Exponential Functions
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...)
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(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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