# Lesson

```Commonly used for the
growth of population of
animals, societies, and
bacteria
Exponential Growth and Decay
Modeling
Ex-Pun-Entail
(Entails extreme puns)
(Models were not harmed in the making of this PowerPoint)
Exponential Population Model
Commonly used for the growth of population of animals, societies, and bacteria
P = Population
t = Time
P0 = Initial Population
r = Rate of growth as a decimal
If r &gt; 0 then the function is exponential growth
If r &lt; 0 then the function is exponential decay
Examples of the Population Model
If Wisconsin Rapids in 1913 had 3000
people (don’t quote me), and the
population grew about 8% per year what
would the population be in 2013?
Examples of the Population Model
(cont.)
Plug in the values into
the equation
=6,599,284 people
Solve the equation
Bacteria Growth Model
Examples of the Bacteria Growth
Model
• Plaque (bacteria on the tooth) can build up on
the teeth if the toothbrush or floss does not
reach a certain section of the tooth. If 10
bacteria start on the tooth and doubles every
hour, how much bacteria will be on the tooth
in 3 days?
Examples of Bacteria Growth Model
cont.
10 &times; 272
Plug in the equation
10 &times; 272 = 4.7223665 &times; 1022
Multiply it through
Decay Model
Example of The Decay Model
• A calm evacuation was announced throughout
the city of Towncityville, AL. The people of the
city were chosen at random to be evacuated
per day. The amount of people evacuated
increased by 2% per day. If the population
started out as 1,000,000 people, what was the
population after 6 days?
Example of Decay Model (cont.)
• Input the variables into the equation
= 8858423.80864
Solve the equation