EXPONENTIAL FUNCTIONS A BRIEF OVERVIEW

EXPONENTIAL FUNCTIONS

EXPONENTIAL GROWTH AND ITS GRAPH a)Exponential growth; b= 1.2 b)Exponential decay; b = ⅔ c)Exponential growth; b= 2. As long as the coefficient a is positive, the function is defined by the value of b.

EXPLORING THE END BEHAVIORS AND ASYMPTOTES

GRAPHING EXPONENTIAL GROWTH FUNCTION xy Directions: 1)Make a table of values 2)Plot the ordered pairs 3)Draw a smooth curve connecting the points 4)Label the asymptotes

EXPLORING THE END BEHAVIORS AND ASYMPTOTES

GRAPHING EXPONENTIAL GROWTH FUNCTION xy Directions: 1)Make a table of values 2)Plot the ordered pairs 3)Draw a smooth curve connecting the points 4)Label the asymptotes

GRAPHING EXPONENTIAL DECAY FUNCTION Directions: 1)Make a table of values 2)Plot the ordered pairs 3)Draw a smooth curve connecting the points 4)Label the asymptotes xy

Writing Equation of the Exponential Function when given two points on the curve.

A: amount at the end P: amount at the beginning r: rate of increase or decrease in decimal T: time in years

Ex. 1 The population of the United States in 1994 was about 260 million with an average annual rate of increase of about 0.7%. A) Find the growth factor. B) Suppose the rate of growth had continued to be 0.7%. Write a function to model this population growth. C) Estimate the population in 2000.

ANSWERS a) Since the rate of increase is 7%, every year the population will grow by 107%. So the growth factor is 1.07.

Finding the average rate of increase or decrease over time. In 1970 the population of Los Angeles was about million people. In 2010, the population was about million people. Find the rate of increase in population for the county of Los Angeles from 1970 to 2010.