2. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models Curve Fitting with Exponential and Logarithmic Models Holt Algebra 2Holt McDougal Algebra 2 How do we model data by using exponential and logarithmic functions? How do we use exponential and logarithmic models to analyze and predict?

3. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models Analyzing data values can identify a pattern, or repeated relationship, between two quantities. Look at this table of values for the exponential function f(x) = 2(3 x ).

4. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models For linear functions (first degree), first differences are constant. For quadratic functions, second differences are constant, and so on. Remember! Notice that the ratio of each y-value and the previous one is constant. Each value is three times the one before it, so the ratio of function values is constant for equally spaced x-values. This data can be fit by an exponential function of the form f(x) = ab x.

5. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models Determine whether f is an exponential function of x of the form f(x) = ab x. If so, find the constant ratio. Identifying Exponential Data 1. x –10123 f(x)f(x) 235812 2. x –10123 f(x)f(x) 1624365481 First Differences Second Differences Ratio 81 54 = 36 = 24 16 = 36 24 = 3 2 Second differences are constant; f is a quadratic function of x. This data set is exponential, with a constant ratio of 1.5. 1234 8121827 111469

6. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models Determine whether f is an exponential function of x of the form f(x) = ab x. If so, find the constant ratio. Identifying Exponential Data First Differences Second Differences Ratio This data set is exponential, with a constant ratio of 1.5. First differences are constant; y is a linear function of x. 1.34234.5 5555 0.6611.5 3. x –10123 f(x)f(x) 2.646913.5 4. x –10123 f(x)f(x) –3271217 13.5 9 = 9 6 = 6 4 = 3 2 4 2.6 =

7. Holt McDougal Algebra 2 Curve Fitting with Exponential and Logarithmic Models Lesson 15.2 Practice A