6.4 Applications of Exponential Functions
This is a set of guiding questions for creating your own lesson plan on applications of
exponential functions.
Learning Objectives
 To apply mathematical models that use basic exponential functions.
 To solve basic equations involving exponential functions using graphs.
Guiding Questions
 What have we learned about exponential functions?
 What is a basic model of an exponential function? (y = bx)
 What restrictions do we put on the base? Why?
 What is the domain of those functions?
 What is the range?
 How is the graph of a basic exponential function (and its range) affected when we
multiply it by a positive integer? How about a negative integer?
 How can we generalize this? (y = abx)
 What happens to y = abx when x = 0?
 What do you think we can predict with these functions?
 Can we represent growth or decay? How?
 If we let x represent time, what would a be? What about y? What about b?
 How and why do we count the population of North Carolina? The United States? The
world?
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1 𝑥
How can we solve the equation 2𝑥 = −𝑥 + 11? What about 3𝑥 + 26 = 5 (2) ?
Would you like to try graphs? How would that help?
Notes for Teachers
 You may want to graph those functions using an online graphing calculator, like the
Desmos. You can graph several graphs with different colors on the same coordinate
axis.
Video of the Day
 6.4.1 Why is the growth/decay factor equal to 1 + rate of growth/decay?
o Description: We answer this question, which often befuddles students.
o Tags: exponential growth, exponential decay, growth rate, decay rate
 6.4.2 How can we solve the equation 2𝑥 = −𝑥 + 11?
o Description: We use a graphing approach to solve this equation, which is
particularly valuable if students have not encountered logarithms.
o Tags: exponential equations, system of equations, graphing method
Some Problems
1) The foundation of your house has about 1,200 termites. The termites grow at a rate of
about 2.4% per day. What will the population of termites be in 5 days?
2) You buy a new computer for $2100. The computer decreases by 45% annually. What
will be its value in 3 years?
3) You have inherited land that was purchased for $30,000 in 1960. The value of the land
increased by approximately 5% per year. What is the approximate value of the land in
the year 2016?