13.3 13.4 Notes Base e and Compound Interest November 16, 2016 13.3 The Base e 13.4 Compound Interest Today we are going to: • Graph and Analyze f(x)=e x • Solve problems involving compound interest • Graphing and Analyzing f(x)=e x Find the e x button on your calculator and use it to find the value of e 1 . e 1 = ___________________ Given the function complete the table below. x 1 10 100 10,000 100,000 1,000,000 ... f(x) ... 13.3 The Base e
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13.3 13.4 Notes Base e and Compound Interest November 16, 2016
13.3 The Base e13.4 Compound Interest
Today we are going to:
• Graph and Analyze f(x)=ex
• Solve problems involving compound interest
• Graphing and Analyzing f(x)=ex
Find the ex button on your calculator and use it to find the value of e1. e1 = ___________________
Given the function complete the table below.
x 1 10 100 10,000 100,000 1,000,000 ...
f(x) ...
13.3 The Base e
13.3 13.4 Notes Base e and Compound Interest November 16, 2016
If you graph f(x) and the horizontal line y = e, you can see that y = e is the horizontal asymptote of f(x).
Even though e is an irrational number, it can be used as the base of an exponential function. The number e is sometimes called the natural base of an exponential function and is used in scientific and other applications involving exponential growth and decay.
1.Graph the function f(x)=e and answer the questions.x
Domain:
Range:
Asymptote:
Increasing or Decreasing?
End Behavior:
13.3 13.4 Notes Base e and Compound Interest November 16, 2016
Describe the transformations of each function, then graph the function. State the domain and range in interval notation.
2.
Domain:
Range:
Asymptote:
3.
Domain:
Range:
Asymptote:
13.3 13.4 Notes Base e and Compound Interest November 16, 2016
4. The Dow Jones index is a stock market index for the New York Stock Exchange. The Dow Jones index for the period 19802000 can be modeled by VDJ(t)=878e0.121t, where t is the number of years after 1980. Determine how many years after 1980 the Dow Jones index reached 3000.
Solve each problem using a graphing calculator. Then determine the growth rate or decay rate of the function.
Modeling with Exponential Functions Having Base e
5. The Nikkei 225 index is a stock index for the Tokyo Stock Exchange. The Nikkei 225 index for the period 19902010 can be modeled by VN225(t)=23,500e0.0381t, where t is the number of years after 1990. Determine how many years after 1990 the Nikkei 225 index reached 15,000.
13.3 13.4 Notes Base e and Compound Interest November 16, 2016