Essential Question: How do you find a growth factor and a decay factor?

An exponential function is a function with the general form y = abx, with the following rules:a 0b > 0 and b 1x is a real numberWhen b > 1, b is called the growth factor

Graphing Exponential GrowthExample: Graph y = 2xStep 1: Make a table of valuesStep 2: Graph the coordinates with a smooth curve

x2xy-32-31/8 = 0.125-22-21/4 = 0.25-12-11/2 = 0.50201121222243238

If you know the rate of increase r, you can find the growth factor by using the equation b = 1 + rExample: In 2000, the population was 281 million and the annual rate of increase in the US population was about 1.24%. Suppose that increase continues to be 1.24%. Which function best models US population growth, in millions, after 2000?281 + 1.0124xHints:281(1.24)x281(1.024)x281(1.0124)x#1) Remember the form y = abx#2) What is 1.24% written as a decimal?

Using the function from the previous slidey = 281(1.0124)xPredict the US population in 2015 to the nearest million Suppose the rate of population increase changes to 1.4%. Write a function to model population growth and then use it to predict the 2015 population to the nearest million. 281(1.0124)15 338 million281(1.014)15 346 million

An exponential function is a function with the general form y = abx, with the following rules:a 0b > 0 and b 1x is a real numberWhen 0 < b < 1, b is called the decay factor

Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay YOUR TURN: Without graphing, determine whether the following functions represent exponential growth or exponential decayy = 100(0.12)xy = 0.2(5)xy = 16()x Since b < 1, this function represents exponential decayExponential decayExponential growthExponential decay

AssignmentPage 434 435Problems 1 9, 17 31 (odd problems)