1. Questions
2. Quiz
3. Review
4. Graphing
Graphs of Inverses
Polynomial Graphs
Intersections of Graphs: Populations, Models
Math as a predictor
Graph Challenge
-Define: Trees and Nature, Graph 2^x
-Penny problems and the King. Unexpected growth
-Birthday problem revisited:
*365!/(365^n)(365-n)! 6. Growth and Decay factors:
1. Bacteria and the oil spill: 12 minute per fission Start with 2 pounds of oil eating bacteria. How long before you have 1,000,000 tons of bacteria?
2. What if only half survive? Death rate, etc..
3. Decay: Credite card debt causes you to lose 15% of your money per month. How long before your 1 million dollar nest egg is less than $500? 4. Is there an easier way to solve M = 1,000,000(.85)^m ? 7. Find the growth or decay rate given a table: 8. Half life, Double rate 9. Geometry: Circles, Area, Triangle problems 10. Review: Modular Arithmetic: You are a construction manager. You need to buy a million nails. They come in boxes with 12,000 nails, which cost 1 cent per nail, and a smaller box with 300 in them that cost 1.5 cents per nail, and a small box with 10 nails per box that costs 2 cents per nail. How many of each boxes should you buy? How many nails will you have over the 1 million? How much will you spend? 11. Growth and Decay rate revisited: Percent growth
-You earn 5% per year on your IRA. What is the growth rate?
-Continuous growth rate: (1 + r/n)^n A = Pe^(rt) e=2.72 12. Problems: You put $1500 into an IRA that earns an interest rate o 4.8% compounded monthly. What is the effective rate?
Compare A = 1500(1 + .048/12)^12t with A = b^t. Solve for b (1.04907) 13. How much money would you lose if you invested $25,000 at 4.5 percent compounded quarterly versus an account that also offered 4.5 percent but was compounded continuously? Assume you left the money in the bank for 20 years. 14. What do we need? Birthday problem: Solve the number of students you need before you get a probability of .5 of having the same birthday. How long will it take for your million to shrink to $500? How much time will it take to get a million tons of bacteria? How do you solve for a variable that is in the exponent position, other than graphing or a table?? LOGS 15. What is a log? A log base? 2^t = 2,000,000,000 Solve for t