Exponential Growth Functions Doubling Time Fitting Exponential to

Exponential Growth Functions Doubling Time; Fitting Exponential to Two Points All slides in this presentations are based on the book Functions, Data and Models, S. P. Gordon and F. S Gordon ISBN 978 -0 -88385 -767 -0

Doubling Time of Niger’s Population • • p. 2

Doubling time of exponential growth • In general, the doubling time t for any exponential growth process is the same at any point on the curve • If you pick up any point (t, y) on the curve, the height y will always increase to 2 y after t time units. p. 3

Doubling time of world population The world’s population grows exponentially, with annual growth rate of 1. 2%, and it has a doubling time of about 58 years The population in 2019 is about 7. 7 billion people § How much will it be in 2077? § When will it be about 30. 8 billion people? p. 4

Example 6: Doubling Time Example 6 Estimate the doubling time for the population of Niger using the equation: Solution Enter the equation Intersection of Adjust window Since we are two curves is (Why these values? ) interested when p(t) solution will double, 2 times 11. 4 is 22. 8 Find the value of x where lines intersect p. 5

Solving Equations Graphically: TI 83/84 Example 5 Estimate when the population of Niger will reach 18 million if the population (Assume t = 0 is the year 1999) of Niger is represented by: Solution Enter the equation ! Adjust window Since we are interested when p(t) (Why these values? ) will be 18, we write @ a second equation Intersection of two curves is solution % Find the value of y where lines intersect ` è 5 p. 6