1. COLLEGE ALGEBRA 5.4. Exponential Growth + Decay

2. Do Now: What is the equation of the tables shown below?

3. Homework Questions??? Comments? Confusions? Concerns? ASK ASK ASK ASK!

4. Exponential Functions We can get the equation from a table We can get the equation from a graph We can graph them ourselves Well….. Just with linear functions we can also have word problems!

5. Exponential Function Word Problems Exponential Functions are often used to model things that change as a set percentage rate over time.

6. **Realize: We’ve already run into these set percentage rate over time Doubling is a 100% increase (New Amount = 200% of what you started with) Tripling is a _______ increase (New amount = ______ of what you started with) Cutting in half is a __________ (New amount = ______ of what you started with)

7. **Realize: We’ve already run into these set percentage rate over time Doubling is a 100% increase (New Amount = 200% of what you started with) Tripling is a 200% increase (New amount = 300% of what you started with) Cutting in half is a 50% decrease (New amount = 50% of what you started with)

8. Exponential Growth vs. Decay

9. Basic Example: Find the equation if we start with 100 items and …. We double the rate We triple the rate We half the rate

10. Words that indicate Growth Increase Grow Appreciate Earning

11. Words that indicate Decay Decreasing Decay Depreciate Spending

12. Example Two: The population of Johnson City in 2005 was 25,000. Since then, the population has grown at an average rate of 3.2% per year. Write an equation to represent the population of Johnson City since 2005. Based on the equation you wrote, what will the population of Johnson City be in 2015?

13. Example Three:

14. You Try!

15. Decaying- Example Four: A fully inflated child’s raft for a pool is losing 6.6% of its air every day. The raft originally contained 4,500 cubic inches of air. Write an equation to represent the loss of air over time Estimate the amount of air in the raft after 7 days.

16. Example Five: The population of Campbell County, Kentucky, has been decreasing at an average of about 0.3% per year. In 2000, its population was 88,647. Write an equation to represent the population since 2000. If the trend continues, predict the population in 2010.

17. You Try!

18. Do Now: In your folder you will find the exponent quiz. Go through it. Where did you go wrong? Do you have questions about it?

19. Depreciation Lots of things you own depreciate over time– this means that as they get older, they lose value. What things can depreciate over time?

20. Example Six: The original price of a tractor was $45,000. The value of the tractor depreciates at a steady rate of 12% per year. Write an equation to represent the value of the tractor since it was purchased. What is the value of the tractor in 5 years?

21. Example Seven: Leonardo purchases a car for $18, 995. The car depreciates at a rate of 18% annually. After six years, Manual offers to buy Leonardo’s car for $4,500. Should Leonardo sell the car? Why or why not?

22. You Try! Mr. Gossell is a machinist. He bought some new machinery for about $125,000. He wants to calculate the value of the machinery over the next 10 years for tax purposes. If the machinery depreciates at the rate of 15% per year, what is the value of the machinery (to the nearest $100) at the end of 10 years?

23. Example Eight: Realize: Appreciation is the opposite of depreciation! It means the value increases as it ages. Mr. and Mrs. Boyce bought a house for $96,000 in 1995. The real estate broker indicated that houses in the area were appreciating at an average annual rate of 7%. If the appreciation remained steady at this rate, what was the value of the Boyce’s home in 2009?

24. You Try! Theo purchased a rare coin from a dealer for $300.00. The value of the coin is expected to appreciate 5% each year. Determine the value of the coin after 5 years? What about after 10 years? Was it a smart investment?

25. Quick Final Thought: Growth or Decay?

26. Quick Final Thought: Growth or Decay?

27. Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me questions if you are confused! Or ask your table mates! They are your greatest resource!

28. Exit Ticket: The number of people who own computers has increased 23.2% annually since 1990. If half a million people owned a computer in 1990, predict the number of people who will own a computer in 2015.