The document discusses exponential growth functions and provides an example of using an exponential growth equation to model and predict population changes over time. Specifically, it shows how to write an equation modeling the 3.2% annual population growth of Johnson City, TN since 2010, and then uses that equation to calculate that the predicted population in 2020 will be around 34,256 people.

1. APPLICATION OF
EXPONENTIAL
FUNCTIONS

2. EXPONENTIAL GROWTH
The general equation for exponential growth is y = C(1 + r)^t.
• y represents the final amount.
• C represents the initial amount.
• r represents the rate of change expressed as a decimal.
• t represents time.

3. TRY THIS EXAMPLE
The population of Johnson City in 2010 was 25,000. Since then, the
population has grown at an average rate of 3.2% each year.
1.Write an equation to represent the population of Johnson City since 2010.
2. According to the equation, what will the population of Johnson City be in
the year 2020?

4. WRITING THE EQUATION
Write an equation to represent the population of Johnson City since 2010.
• The rate 3.2% can be written as 0.032. C is the initial value.
• y = C(1 + r)^t
• y = 25,000 (1 + 0.032)^t
• y = 25,000 (1.032)^t

5. POPULATION IN 2020
According to the equation, what will the population of Johnson City be in the
year 2020?
• In 2020, t will equal 2020 - 2010 or 10.
• Substitute 10 for t in the equation.
• y = 25,000(1.032)^10
• y = 34,256
In 2020, the population of Johnson City will be about 34,256.