Exponential Functions, Growth and Decay

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

2. 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.

3. 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 exponential function is f (x) = bx, where the baseb is a constant and the exponent x is the independent variable.

4. The graph of the parent function f(x) = 2xis shown. The domain is all real numbers and the range is {y|y > 0}.

5. 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.

6. Remember! Remember! Negative exponents indicate a reciprocal. For example: In the function y = bx, y is a function of x because the value of ydepends on the value of x.

7. Recognizing Exponential Growth Functions State whether the function represents exponential growth or exponential decay. exponential growth exponential decay exponential decay

8. Recognizing Exponential Growth Functions State whether the function represents exponential growth or exponential decay. exponential growth exponential growth

9. Graphing Exponential Growth Functions Graph the function. HA:

10. Graphing Exponential Growth Functions Graph the function. HA:

11. Graphing Exponential Growth Functions Graph the function. HA:

12. Graphing Exponential Growth Functions Graph the function. HA:

13. Lesson 8.1 Practice A