Exponential and Logarithmic Functions

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Presentation transcript:

Exponential and Logarithmic Functions Chapter 8 Exponential and Logarithmic Functions

Please take out your iPad Using Desmos, graph the following equation: Y = 2x Discuss with your neighbor the shape and direction of this graph. Without erasing previous graphs, add the graphs of Y = 5x Y = .5x Make a list of similarities and differences.

8-1Exponential Models

8-1Exponential Models

Write an exponential function for the graph which goes through (0,2) and (1, 1.3)

8-1Exponential Models

8-1Exponential Models

8-1Exponential Models

8-1Exponential Models

An exponential function takes the form Y = abx the “a” represents the initial or beginning value The “b” represents the growth or decay rate If the function is increasing b = 1 + r If the function is decreasing b = 1 – r Where r is the rate of change as a decimal DO NOT multiply a and b together!

8-1Exponential Models

8-2 Properties of Exponential Functions

8-2 Properties of Exponential Functions Principal: $5000, interest rate 6.9%, 30 years Principal: 20,000, interest rate 3.75%, 2 years

8-2 Properties of Exponential Functions

8-3 Logarithmic Functions What exponent would you have to use to: change 2 to 8? change 7 to 1? change 5 to 25? change 3 to 81? change 4 to 0.25? When you are determining the exponent you would need to change a number to something else, you are finding the logarithm. Logarithms are exponents.

8-3 Logarithmic Functions

8-3 Logarithmic Functions

8-3 Logarithmic Functions

8-3 Logarithmic Functions

8-3 Logarithmic Functions Evaluate each logarithm

8-3 Logarithmic Functions

8-3 Logarithmic Functions Sometimes you will need to convert each number to a power of the same base.

8-4 Properties of Logarithms

8-4 Properties of Logarithms

8-4 Properties of Logarithms

8-5 Exponential and Logarithmic Equations

8-5 Exponential and Logarithmic Equations

8-5 Exponential and Logarithmic Equations

Change of Base Formula

Logarithmic Equations

Change of Base Formula

warm up

8-6 Natural Logarithms

8-2 Properties of Exponential Functions

An initial population of 450 quail increases at an annual rate of 9% An initial population of 450 quail increases at an annual rate of 9%. Write an exponential function to model the quail population. The half life of a certain radioactive material is 60 days. The initial amount of the material is 785 grams. Write an exponential function to model the decay of this material. Write the exponential function that contains the points (0,6) and (1,12)