1. 7.4 B – Applying calculus to Exponentials

2. Big Idea This section does not actually require calculus. You will learn a couple of formulas to model exponential growth and decay that were found using calculus. You do not have to derive the formulas, you can simply use them to solve the problems.

3. Exponentials.

4. Money Application A = Pe rt

5. Example

6. Population Problems Equation: Population = Initial (base) (1/time to increase)time We can choose a convenient base to help figure out a growth pattern.

7. Example

8. Continued

9. The equation for the amount of a radioactive element left after time t is: If k 0 it is growth. The half-life is the time required for half the material to decay. Radioactivity Application

10. 60 mg of radon has a half-life of 1690 years. How much is left after 100 years? Example

11. 100 bacteria are present initially and double every 12 minutes. How long before there are 1,000,000 You try!

12. Half-life Half-life: Equation for Half-Life (you do not need to write this work)

13. Warm Up

14. Coffee left in a cup will cool to the temperature of the surrounding air. The rate of cooling is proportional to the difference in temperature between the liquid and the air. This observation is Newton’s Law of Cooling, although it applies to warming as well, and there is an equation for it. Newton’s Law of Cooling

15. Formula

16. Example

17. Continued

20. Homework Page 361: 15, 21, 22, 24, 32