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8.3 The natural base e. Definition of e e 2.718281828459.

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Presentation on theme: "8.3 The natural base e. Definition of e e 2.718281828459."— Presentation transcript:

1 8.3 The natural base e

2 Definition of e e

3 The Graph of the Natural Base Function y = ae x-h + k Graph Natural base function.tiiNatural base function.tii

4 The Graph of the Natural Base Function y = ae x-h + k Exponential function Natural base function This function is an exponential function. The a, h, k function the same. * a changes the distance from the asymptote to the y-intercept. h shifts the graph horizontally. k shifts the graph vertically.

5 The Graph of the Natural Base Function y = ae x-h + k Exponential function Natural base function Exponential growth, b > 1 ( With a positive x.) * Exponential growth, e is greater than one with a positive x. * Exponential decay b is greater than 0 but less than one. (With a positive x.) * e is fixed so multiplying x by a negative number produces a decay.

6 Problems - Simplifying

7 Compound Interest Problem Recall for the compound interest formula for interest compounded n times a year. For continuous compounded (compounded all the time) we use the following formula. A = balance P = principle r = %/100 t = years

8 Interest Problem You deposit $975 in an account that pays 5.5% annual interest compounded continuously. What is the balance after 6 years?


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