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Chapter 1 Prerequisites for Calculus - Coggle Diagram

- - - - Exponential Growth and Decay: The equation to find compound interest would be A = A.(1+i/n)^(nt). Compound interest formula would be used to find deposits or loans which in general would be interest so it would usually be used in word problems relating to money. This equation gives you the answer to A which is the future amount and using the Initial amount (A.) times the bracket of 1 + interest rate, percent changed into decimals, over n which is how it is compounded, annually, semiannually, quarterly, monthly, and daily. Then the bracket to the power of n times the number of years. To find the time using this equation, you would need to isolate t so first move the A initial and simplify whatever is possible. Then use log to isolate t and then use the base rule of log to isolate t.
      - Exponential Growth and decay: This equation follows the change using the formula A = A. (B)^(T/P). Similarly to the past formulas in exponential applications, the A and A. is the future and initial amount and then t would be the time. This equation is different from the others as there are two different variables present which are B and P. B means that type of growth which would mean half life which is 1/2, doubles which is 2, etc. and P would be the period of growth to occur so the initial time.
      - Compound Interest Continuously: Compound interest continuously, relates to interest that would be continuous so to find the continuous amount which is the future amount, it would be A = A. (e) ^ (it). Similarly to compound interest, the future amount and initial amount are represented by the same variable and same with time and interest rate but there is a change as e is present. e is a mathematical constant that which is the number 2.71828 and is a natural log.