FUNDAMENTALS OF ALGEBRA 2A CHAPTER 8 POWERPOINT PRESENTATION

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Presentation transcript:

FUNDAMENTALS OF ALGEBRA 2A CHAPTER 8 POWERPOINT PRESENTATION EXPONENTIAL AND LOGARITHMIC FUNCTIONS

LEARNING TARGETS AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: EVALUATE GRAPHS OF EXPONENTIAL FUNCTIONS USE SCIENTIFIC NOTATION IN COMPUTATIONS EXPRESS TRANSLATIONS OF EXPONENTS AND LOGARITHMS EVALUATE LOGARITHMIC FUNCTIONS SOLVE EQUATIONS WITH LOGARITHMS

EXPONENTIAL GROWTH

Exponential Functions

EXPONENTS WITH A BASE OF 10

SCIENTIFIC NOTATION REDUCING A LARGER NUMBER TO WHERE IT IS MORE THAN ONE BUT LESS THAN TEN ALSO WITH A POWER OF 10. 5,625,000 = 5.625 x 10⁶ .005689 = 5.689 x 10¯³

Exponential Equations THESE ARE EQUATIONMS THAT YOU SOLVE WHICH INVOLVE EXPONENTS THAT ARE DECIMALS, OR POWERS.

The Number e, Base e The number e is an irrational number, which means the decimal is non-repeating and non-terminating. The number e is like the symbol used for the number that is represented by pi:

Inverse Functions Inverse means the opposite. Suppose you have a set of ordered pairs: (1,2), (2,3), (4,5), (10, 40), the domain (x) values are: 1, 2, 4, 10 and the range (y) values are: 2, 3, 5, 40. In an inverse function, you interchange the x and y values: (2,1), (3,2), (5, 4), and (40, 10).

Logarithms A number showing the power to which a certain fixed number (the base), must be raised to yield a specified number. If you write 10² the base is ten and the exponent is 2. 10² also means log10 – 100 = 2, which is read logarithm base 10 of 100 equals 2.

Logarithmic Functions The laws of operation with logarithms are the same as those for exponents. Logarithms:

Logarithms Logarithms are used to calculate (mortgages, payments, earnings, etc.):