8.1 Exploring Exponential Models

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Presentation transcript:

8.1 Exploring Exponential Models Few things are impossible to diligence and skill. Great works are performed not by strength, but perseverance.

Exponential Equations An exponential function is a function with the general form , where x is a real number, , , and . When , b is the growth factor and you can use the exponential function to model growth. Ex1) Graph: Step 2: plot points and connect x 2x y -3 2-3 -2 2-2 -1 2-1 20 1 21 2 22 3 23

Application Example If you know the rate of increase r, then the growth factor b = 1 + r. Ex2) The population of the United States in 1994 was almost 260 million with an average annual rate of increase of about 0.7%. a. Find the growth factor for that year. b. Suppose the rate of growth had continued to be 0.7%. Write a function to model this population growth. c. Predict U.S. population in 2015 to the nearest million.

Additional Example ~ You Try… Ex3) Write an exponential function y = abx for a graph that includes (2, 4) and (3, 16).

Graphing Exponential Decay When , b is the decay factor and you can use the exponential function to model decay. Ex4) Graph y = 36(0.5)x. Identify the horizontal asymptote. Step 1: Make a table of values. x –3 –2 –1 0 1 2 3 y Step 2: Plot points and connect An asymptote is a line that a graph approaches as x or y increases in absolute value.

Exponential Equations Ex 5) Determine whether each function represents exponential growth or decay. What is the percent of increase or decrease? Ex 6) For each annual rate of change, find the corresponding growth or decay factor.

Application Example Ex7) Suppose you buy a used car that costs $11,800. After one year the value of the car is $9,440. Estimate the depreciated value of the car after 6 years.

8.1 Exploring Exponential Models HW: 1, 7-27 odd, 35-41 all, 46-53 all Few things are impossible to diligence and skill. Great works are performed not by strength, but perseverance.

Exponential Equations Ex 4) Determine whether each function represents exponential growth or decay. What is the percent of increase or decrease? Ex 5) For each annual rate of change, find the corresponding growth or decay factor.