1. Exponential Growth

2. Definition: Growing without bound. Ie. Nothing limits the growth.

3. What does it look like?

4. Population Independent Axis Dependent Axis

5. Population is a function of time:

6. Population: Write down the first thing you think of when you hear the word “population”. Not a definition, just the first thing that pops into your head.

7. Population: A population can be: People Rust Bacteria Rocks Anything that can be grouped and categorized.

8. Example A population of people increases from 2500 to 2700 in 25 years. What is the growth rate constant for this population?

9. Example A population of bacteria doubles every 43 minutes. What is the growth rate constant?

10. Logistic Growth and Exponential Decay

11. Logistic Growth Logistic growth is where a population is growing toward a maximum number that is allowed for that population. In other words, a population that is growing logistically has limitations.

12. What does it look like?

13. Populations Populations can’t grow exponentially forever. What factors inhibit growth?

14. Factors that inhibit growth Size of the area (overpopulation) Disease Predators Natural Disasters Man-made disasters War

15. Limit of Growth When a population reaches its maximum number, we say that the population has met its: Carrying capacity

16. Logistic Modeling The growth model for a population that grows logistically is:

17. Example The number of fruit flies in a population after t days can be found by the equation:

18. Example (cont.) What is the carrying capacity?

19. Example (cont.) What is the initial population?

20. Example (cont.) What will the population be after 15 days? After 30 days?

21. Decay Exponential decay is normally discussed in terms of radioactive decay. We model decay with the equation:

22. Decay Decay is normally discussed in reference to a half-life. A half-life is the time it takes for half of the material to decay.

23. Example A certain drug that a patient must receive has a half life of 13 days. If it is no longer potent once it has reached 40% of its original mass, how long after production does the doctor have to administer the drug?