Exponential Functions Growth and Decay Growth and How

Exponential Functions, Growth, and Decay Growth and • How do we write and evaluate exponential expressions to model growth and decay situations? Holt. Mc. Dougal Algebra 2 Holt

Exponential Functions, Growth, and Decay Moore’s law, a rule used in the computer industry, states that the number of transistors per integrated circuit (the processing power) doubles every year. Beginning in the early days of integrated circuits, the growth in capacity may be approximated by this table. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Growth that doubles every year can be modeled by using a function with a variable as an exponent. This function is known as an exponential function. The parent x exponential function is f (x) = b , where the base b is a constant and the exponent x is the independent variable. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay The graph of the parent x function f(x) = 2 is shown. The domain is all real numbers and the range is {y|y > 0}. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay A function of the form f(x) = abx, with a > 0 and b > 1, is an exponential growth function, which increases as x increases. When 0 < b < 1, the function is called an exponential decay function, which decreases as x increases. Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Remember! In the function y = bx, y is a function of x because the value of y depends on the value of x. Remember! Negative exponents indicate a reciprocal. For example: Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Recognizing Exponential Growth Functions State whether the function represents exponential growth or exponential decay. exponential growth exponential decay Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Recognizing Exponential Growth Functions State whether the function represents exponential growth or exponential decay. exponential growth Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Graphing Exponential Growth Functions Graph the function. HA: x y Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Graphing Exponential Growth Functions Graph the function. HA: x y Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Graphing Exponential Growth Functions Graph the function. HA: x y Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Graphing Exponential Growth Functions Graph the function. HA: x y Holt Mc. Dougal Algebra 2

Exponential Functions, Growth, and Decay Lesson 8. 1 Practice A Holt Mc. Dougal Algebra 2