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8.3 The natural base e

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Definition of e e

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**The Graph of the Natural Base Function y = aex-h + k**

Graph Natural base function.tii

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**The Graph of the Natural Base Function y = aex-h + k**

Exponential function Natural base function This function is an exponential function. * a changes the distance from the asymptote to the y-intercept. h shifts the graph horizontally. k shifts the graph vertically. The a, h, k function the same.

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**The Graph of the Natural Base Function y = aex-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.

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**Problems - Simplifying**

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**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

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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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