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Transcendental Functions

This guide explores the concepts of exponential and logarithmic functions, focusing on growth rates such as y = 2^x and y = (1/2)^x. It explains the natural exponential function, y = e^x, and provides the continuous compounding interest formula. Using a practical example, we calculate how much Johnny's $5000 investment at a 5.2% interest rate, compounded quarterly, will grow over 10 years. Equipped with the compound interest formula, you’ll understand how to determine the final amount in any investment scenario.

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Transcendental Functions

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  1. Transcendental Functions Exponential and Logarithmic Functions

  2. y = ax Growth Rate

  3. y = 2x y = 4x “Parent” y = (1/2)x y =2-x

  4. Translations

  5. Natural Exponential Function y = ex Growth Rate

  6. Continuous Compounding Interest Formula Use this formula whenever the growth in “compounding continuously”.

  7. Johnny invested $5000 in an account earning 5.2% interest compounded quarterly. If left untouched, how much will be in the account in 10 years?

  8. Compound Interest Formula Time in years Final amount Beginning amount Interest Rate # of Times a year compounded

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