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Simplifying Exponential Functions and Graphing Techniques

Explore the properties of exponents and learn to simplify expressions effectively. This guide provides step-by-step examples similar to homework problems, including sketching graphs for various functions and determining horizontal asymptotes. Additionally, it covers tables for calculating investment balances and the necessary principal amounts to achieve specific financial goals compounded at different rates. You’ll also discover how to find effective interest rates based on nominal rates compounded annually, semiannually, quarterly, and monthly.

keegan-avila
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Simplifying Exponential Functions and Graphing Techniques

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  1. Natural Exponential Functions

  2. 1. Use the properties of exponents to simplify the expression(Similar to p.264 #1-4)

  3. 2. Use the properties of exponents to simplify the expression(Similar to p.265 #1-4)

  4. 4. Sketch the graph of the function(Similar to p.265 #7-18)

  5. 5. Sketch the graph of the function(Similar to p.265 #7-18)

  6. 6. Sketch the graph of the function(Similar to p.265 #7-18)

  7. 7. Sketch the function. Determine whether the function has any horizontal asymptotes and discuss the continuity of the function(Similar to p.265 #17-24)

  8. 8. Complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per yearP = $2000, r = 3.2%, t = 15 years(Similar to p.265 #27-30)

  9. 9. Complete the table to determine the amount of money P that should be invested at rate r to produce a final balance of $200,000 in t yearsr = 4.1%, compounded continuously(Similar to p.265 #31-34)

  10. 10. Complete the table to determine the amount of money P that should be invested at rate r to produce a final balance of $200,000 in t yearsr = 2%, compounded weekly(Similar to p.265 #31-34)

  11. 11. Find the effective rate of interest corresponding to a nominal rate of 8% per year compounded (a) annually, (b) semiannually, (c) quarterly, and (d) monthly

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