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5) Unit 6 Exponential Growth.notebook
1
May 19, 2016
ExponentialsExponential Growth
By the end of this lesson you will have an understanding of exponential growth and be able to apply it to real world situations.
Learning Goal
Exponential Growth
• Has a general equation of f(x)=abx where b>1.
• As the xvalues increase by a constant amount the yvalues increase by a common factor.
• The graph increases at an increasing rate.
5) Unit 6 Exponential Growth.notebook
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1 Is this an example of exponential growth?
Yes
No
2 Is this an example of exponential growth?
Yes
No
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3 Is this an example of exponential growth?
Yes
No
Example 1. The following is a graphical model of the doubling function for the bacterium Escherichia coli. This bacterium has a doubling period of 0.32 hours.
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a) Is this function exponential? Explain.
b) What is the yintercept? What does it represent in this situation?
c) What is the domain? What does it represent in this situation?
d) What is the range? What does it represent in this situation?
e) How many bacteria are present after 1 hour?
Example 2. Examine each stage of the pattern below. Complete the table of values and determine an equation that models the situation.
Stage 0 Stage 1 Stage 2 Stage 3Stage Number of Blue Triangles
0
1
2
3
4
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Exponential Growth Applications
A = Final ValueP = Initial Valuer = Growth ratet = Time asked in questiond = Time for growth rate
BasicFormula
4 Determine the growth rate in the following exponential model. Write your answers as a percent.
f(x) = 100(1.048)x
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Example 3. A school has an enrolment of 1200 students. The student population is expected to grow at a rate of 1.5% each year for the next 10 years. Estimate the number of students enrolled 8 years from now.
Example 4. Erinn deposits $100 into a bank account that pays interest at 5% per year, compounded annually. Determine the amount of money that she would have after 30 years.
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Exponential Growth Applications
A = Final ValueP = Initial Valueb = Growth factor (replaces (1+ r))t = Time from questiond = Time for growth factor
TweakedFormula
Optional
5 Determine the intial value in the following equation.
f(x) =200(4)0.5x
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Example 5. A strain of yeast cells triples every hour. Suppose there are 60 cells now how many would there be in 5 hours?
Example 6. Suppose that there is a rumor going around the school that Mr. Perkins is really three ducks dressed up in a man costume. The rumor starts with just one person and he tells 2 people in his class. Through the power of texting the number of new students who hear the rumor doubles every 2 minutes. How long will it take to encounter the texting cycle that informs 1024 new students of the rumor?
Quack
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Homework:Page 261 # 3, 5, 6, 11
