Section 10.4 Exponential Growth and Decay

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

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

Calculus, Section 10.4, Todd Fadoir, CASA, 2005

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

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

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

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

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

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

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

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

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