1. Section 10.4 Exponential Growth and Decay
AP Calculus
March 16, 2009
Berkley High School

2. Constant k is sometimes called the relative growth rate
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

3. Calculus, Section 10.4, Todd Fadoir, CASA, 2005

4. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
Assuming that the growth rate is proportional to population size, use the fact the population in 1900 is 1650 million and the 1910 is 1750 million to find population in the year 2000.
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

5. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

6. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
The half-life of radium-226 is 1590 years (meaning after 1590 years, half of the radium is gone).
A sample of radium has a mass of 100 mg.
Find a formula for the mass of radium after t years.
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

7. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

8. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
The half-life of radium-226 is 1590 years (meaning after 1590 years, half of the radium is gone).
A sample of radium has a mass of 100 mg.
Find the mass after 1000 years.
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

9. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

10. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
The half-life of radium-226 is 1590 years (meaning after 1590 years, half of the radium is gone).
A sample of radium has a mass of 100 mg.
When will the mass be reduced to 30?
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

11. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Example
Calculus, Section 10.4, Todd Fadoir, CASA, 2005

12. Calculus, Section 10.4, Todd Fadoir, CASA, 2005
Exercises
Section 10.4: 1-11 odd
Calculus, Section 10.4, Todd Fadoir, CASA, 2005