1. Exponential Systems

2. Exponential systems We have talked about Exponential Systems before.
Radioactive Decay, population growth, interest earned on a bank account
Exponential systems
We have talked about Exponential Systems before.
Imagine a system where change is dependant on the amount present. That is,
Where t is time and k is a constant.
If we know the initial condition y = y0, then we can find an equation for y based on any t value.

3. If we know the initial condition (when t = 0) then we can determine A

4. Exponential systems
All systems that grow/shrink exponentially fit a general pattern
Where y0 is the initial amount, k is a constant that will often have to be determined and t is time.

5. The rate at which the number of cookies present at C lunch changes is proportional to the number of cookies present.
Time is measured in minutes. If there are 140 cookies on the first tray out (t = 0) how many will be present after 5 minutes.
THAT IS, when t = 5

6. A new problem
The tray of 140 cookies is put out at E lunch. After 2 minutes, only 17 cookies remain. How many will be left after 5 minutes?

7. What was seen here?
In Initial/Later condition problems you will need to find k to continue the problem. This is typical in AP problems.

8. Another Problem
A small amount of radioactive substance is placed in a lead container. After 24 hours it is observed that 6/7 of the substance remains. If the rate of decay is proportional to the amount of substance present at any time, what is the half life? How long will it take for it to be reduced to 1/5 of the original amount?

9. Homework
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