Algebra II Mr. Hartzer, Hamtramck High School 2017-18
DO NOW: SAT Review The weight of an object on Venus is approximately 9/10 of its weight on Earth. The weight of an object on Jupiter is approximately 23/10 of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus? A. 90 B. 111 C. 140 D. 230
This Week’s Questions Ch 7 What are exponential functions? What is a logarithm and a logarithmic function?
Today’s Objective 7-4 I will be able to: apply basic properties of logarithms.
Exponential Function Growth functions have asymptotes to the left; decay functions, to the right.
Exponential Functions • is called an EXPONENTIAL FUNCTION. • All exponential functions have the same basic shape. • goes through and
Asymptote • An asymptote is a line that a function gets closer and closer to. • The horizontal asymptote of is .
Rate of Change • The rate of change is a percentage related to the growth or decay factor. • If , the rate of change is positive. • If , the rate of change is negative.
The Natural Base e e is a constant. On the calculator, press 2nd and then the division symbol.
Rate of Change Formulas Standard: Half-life: Compound interest:
Logarithms If is a positive number other than 1, then:
Different forms (review) Logarithmic: Exponential: Radical:
Special Rules • (because ) • (because )
Common Log so
Natural Log If then
Graphing: b > 1 • RED: • BLUE:
Graphing: 0 < b < 1 • RED: • BLUE:
Change of base formula For all valid logarithms:
Logarithm Properties Product: Quotient: Power: