CHAPTER 6 Differential Equations Calculus AB Homework 6
CHAPTER 6 Differential Equations
Calculus AB Homework 6. 1 Page 411 3 -15 every three, 30, 35, 45, 55, 62 6. 2 Page 420 4 -48 every four (omit 16), 65 6. 3 Page 431: 5 -50 every five, 64, 66, 83 abc, 90
CHAPTER 6 Section 2: Differential Equations- Growth and Decay
Differential Equations •
Separation of Variables •
Differential Equations •
Differential Equations •
Growth and Decay Models •
Growth and Decay Models •
Growth and Decay - Proportions •
Growth and Decay – Half Life • Radioactive decay can be modeled with the same function where y is the current amount at a certain time t. C would be the initial amount. • Half-life is the number of years/amount of time required for half of the atoms in a sample of radioactive material to decay.
Growth and Decay – Half Life C has a half life of 5730 years. • Given an initial quantity of 5 g, after 10000 years, how much carbon remains? • 14 • Given that 3 g remains after 1000 years, what was the initial quantity?
Newton’s Law of Cooling • Newton’s law of cooling uses the same time idea as well. The law states that the rate of change in the temperature of an object is proportional to the difference between the object’s temperature and the temperature of the surrounding medium.
Homework • Page 420 • 4 -48 every four (omit 16), 65
- Slides: 14