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Exponential Growth and Exponential Decay Section 8.1 and 8.2
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### Transcript of Exponential Growth and Exponential Decay Section 8.1 and 8.2.

• Slide 1
• Exponential Growth and Exponential Decay Section 8.1 and 8.2
• Slide 2
• WHAT YOU WILL LEARN: 1.How to graph exponential growth functions. 2.How to graph exponential decay functions.
• Slide 3
• Exponential Growth This is demonstrated by the classic riddle in which a child is offered two choices for an increasing weekly allowance: the first option begins at 1 cent and doubles each week, while the second option begins at \$1 and increases by \$1 each week.
• Slide 4
• Exponential Growth W01234567891011121314151617 1.01.02.04.08.16.32.641.282.565.1210.2 4 20.4 8 40. 96 81. 92 163.84 327.68 655.36 131 0.7 2 2\$1\$2\$3\$4\$5\$6\$7\$8\$9\$10\$11\$12\$13\$14\$15\$16\$17\$18 This is demonstrated by the classic riddle in which a child is offered two choices for an increasing weekly allowance: the first option begins at 1 cent and doubles each week, while the second option begins at \$1 and increases by \$1 each week. Although the second option, growing at a constant rate of \$1/week, pays more in the short run, the first option eventually grows much larger:
• Slide 5
• Why! Exponential Growth! The equation for option 1 is: y = 2 n where n is the number of weeks. The equation for option 2 is y = 1 + n where n is the number of weeks.
• Slide 6
• Oh Boy! Vocabulary An exponential function involves the expression b x where the base b is a positive number other than 1. The variable is going to be in the position of the exponent.
• Slide 7
• Let s Graph an Example Question: Will the graph ever pass below y of 0?
• Slide 8
• Let s Graph an Example Question: Will the graph ever pass below y of 0? We say that there is an asymptote at y = 0.
• Slide 9
• Let s Graph an Example Question: Will the graph ever pass below y of 0? We say that there is an asymptote at y = 0. An asymptote is a line that a graph approaches as you move away from the origin.
• Slide 10
• Try the following on your graphing calculator Group 1:Group 2: How does a in the function affect the graph?
• Slide 11
• A Definition y = ab x is an exponential growth function. When a is greater than 0 and b is greater than 1.
• Slide 12
• Graphing Examples Graph
• Slide 13
• Another Example Graph
• Slide 14
• Graphing by Translation The generic form of an exponential function is: y = ab x-h + k Where h is movement along the x axis and k is movement along the y axis.
• Slide 15
• An Example of Graphing by Translation Graph
• Slide 16
• You Try Graph
• Slide 17
• Exponential Growth Model We will use the formula: y = a(1 + r) t a is the initial amount, r is the percent increase expressed as a decimal and t is the number of years. The term 1 + r is called the growth factor.
• Slide 18
• An Example Problem In January 1993, there were about 1,313,000 Internet hosts. During the next five years, the number of hosts increased by about 100% per year. Write a model. How many hosts were there in 1996? Graph the model. When will there be 30 million hosts?
• Slide 19
• Section 8.2 Exponential Decay These functions will have the form y = ab x where a is greater than zero and b is between 0 and 1. 19
• Slide 20
• Example 1 20 State whether the function is an exponential growth or exponential decay function.
• Slide 21
• You Try State whether the function is an exponential decay or growth function.
• Slide 22
• A Basic Graph A graph of
• Slide 23
• Graphing Exponential Functions again Graph:
• Slide 24
• Another Example Graph:
• Slide 25
• Graphing by Translation The generic form of an exponential function is: y = ab x-h + k Where h is movement along the x axis and k is movement along the y axis.
• Slide 26
• Graphing by Translation Graph:
• Slide 27
• An Exponential Decay Word Problem We will use the formula: y = a(1 - r) t (1-r) is called the decay factor.
• Slide 28
• The Word Problem You buy a new car for \$24,000. The value y of the car decreases by 16% each year. 1. Write an exponential decay model for the value of the car. 2. Use the model to estimate the value after 2 years. 3. Graph the model. 4. When will the car have a value of \$12,000.
• Slide 29
• Homework : Page 469, 14-18 even, 19-24 all, 34, 36, 38, 43-45 all Page 477, 12, 16, 18, 19-24 all, 36, 40, 42, 47-49 all