7.1 EXPLORING EXPONENTIALMODELS Chapter 7: Exponential and Logarithmic Functions
Exponential Functions The general form of an exponential function is where x is a real number, a ≠ 0, b > 0, and b ≠ 1. To graph an Exponential Function: create a table of values and plot the points Example: Graph
Exponential Functions Exponential Functions always have the curved shape They also have an asymptote, a line that the graph approaches but never touches or crosses The domain is all real numbers. The range is y > 0
Exponential Functions There are two types of exponential behaviorExponential Exponential Decay Growth As the value of x As the value of x increases, the value increases, the value of y decreases of y increases
Exponential Functions For the function If a > 0 and b >1, the function represents exponential growth If a > 0 and 0 < b < 1, the function represents exponential decay The y-intercept of the graph is at (0, a) The asymptote is y = 0
Without graphing, determine whether the functionrepresents exponential growth or decay. Then findthe y-intercept.
Exponential Growth and Decay In the function , b represents the growth or decay factor. If b > , then it is the growth factor If 0 < b < 1, then it is the decay factor
Exponential Growth and Decay To model exponential growth and decay we use the following function To use this function: 1. Identify the value of the variables 2. Plug the known values into the equation 3. Solve for the For growth or decay to be exponential,unknown value a quantity changes by a fixed percentage each time period
Example: Page 436 You invested $1000 in a savings account at the end of the 6th grade. The account pays 5% annual interest. How much money will be in the account after 6 years?
Homework P. 439 #1 – 6 all, 8, 10 – 25 odd, 26 (parts a & b), 27, 28