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Understanding the Natural Base Function: e

Explore the definition and graph of the natural base function y = a * e^(x-h) + k, understanding exponential growth and decay, and solving compound interest problems using continuous compounding formula.

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Understanding the Natural Base Function: e

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  1. 8.3 The natural base e

  2. Definition of e e  2.718281828459

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

  4. 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.

  5. 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.

  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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