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The document discusses exponential functions of the form f(x) = a*b^x, explaining that they always have a curved shape and asymptote at y=0. It distinguishes between exponential growth, where the value of y increases as x increases, and exponential decay, where the value of y decreases as x increases. Examples are provided to demonstrate how to determine if a function represents growth or decay and to find the y-intercept.

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7.1 EXPLORING EXPONENTIAL MODELS 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 behavior Exponential 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 function represents exponential growth or decay. Then find the 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

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7.1

  • 1. 7.1 EXPLORING EXPONENTIAL MODELS Chapter 7: Exponential and Logarithmic Functions
  • 2. 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
  • 3. 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
  • 4. Exponential Functions There are two types of exponential behavior Exponential 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
  • 5. 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
  • 6. Without graphing, determine whether the function represents exponential growth or decay. Then find the y-intercept.
  • 7. 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
  • 8. 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
  • 9. 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?
  • 10. Homework P. 439 #1 6 all, 8, 10 25 odd, 26 (parts a & b), 27, 28