08 Bases Other Than e Day 2.notebook April 07, 2014 Recall from last time, Derivative Formulas Involving Logs & Exponential Functions Log Rule Base "e" Log Rule Base "a" Expo. Rule Base "e" Expo. Rule Base "a" Exponential & Log Derivative Formulas Recall: Integral of "e" OR Integrals for base"a" *These formulas you may want to add to your Integrals Note Card!! Integrals of bases other than "e" 1 08 Bases Other Than e Day 2.notebook April 07, 2014 Example: Find the Integral 1. 2. "u" Substitution Examples Compound Interest Let P = pocket $$, t = number of years, r = annual interest rate (convert to a decimal), n = # of times a year interest is compounded A = value of account after t years For interest compounded "n" times a year: For interest compounded continuously: Compound Interest Formulas 2 08 Bases Other Than e Day 2.notebook April 07, 2014 Example: $2500 is invested in an account that has a 7% interest rate. Find the amount of money in the account after 5 years if the account is compounded (a) annually, (b) quarterly, (c) monthly, (d) daily, and (e) continuously A = ??, P = 2500, r = 7% (.07), t = 5 a) Annually means: n = 1 d) Daily means: n = 365 b) Quarterly means: n = 4 e) Conintuously means: A = Pert c) Monthly means: n = 12 Easy Example Example Involving Logs: Compounding monthly at an interest rate of 12%, how long will it take for an account to double in value? It appears we don't have enough information. Let's look at what we do know: • r = 12% (.12), • n = 12, • t=t What do we know about A & P? A will be 2 times P ie: A = 2P Example Involving Logs 3 08 Bases Other Than e Day 2.notebook April 07, 2014 Example Involving Limits Suppose the yield V (in millions of cubic feet per acre) for a stand of timber at age "t" years is found to be: (a) Find the limiting volume of wood per acre as t approaches infinity (ie: ) What happens to the exponent as "t" approaches ∞ the exponent goes to 0 Example Involving Limits Example Involving Derivatives Suppose the yield V (in millions of cubic feet per acre) for a stand of timber at age "t" years is found to be: (b) Find the rate of change at which the yield is changing when t = 20 years and t = 60 years. What does "rate of change" imply?? derivatives!! Example Involving Derivatives 4 08 Bases Other Than e Day 2.notebook April 07, 2014 Homework: p368 (#75-86 all, 95a&b, 105, 108, 121-123) Homework 5

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