1. CHAPTER 5 SECTION 5.5 BASES OTHER THAN e AND APPLICATIONS

2. Definition of Exponential Function to Base a

3. a 0 = 1 a x a y = a x+y a x = a x-y a y (a x ) y = a xy

4. Definition of Logarithmic Function to Base a

6. Properties of Inverse Functions

12. Theorem 5.13 Derivatives for Bases Other Than e

13. Examples for Derivatives for Bases other than e

25. Theorem 5.14 The Power Rule for Real Exponents

26. Differentiate. Hint: Take the ln of both sides.

27. Find each derivative with respect to the given variable.

31. Differentiate. –Using logarithmic differentiation, we have: LOGARITHMIC DIFFERENTIATION

32. To integrate exponential functions other than base e, either Convert to base e using the formula Or  Integrate directly using the integration formula

33. EXP. FUNCTIONS WITH BASE a Example 14

34. Theorem: Proof:

35. Theorem: Proof:

36. Theorem 5.15 A Limit Involving e

37. Applications of Exponential Functions Compound Interest Formulas –Compounded n times per year: –Compounded continuously: Where t = number of years, P = Initial deposit, A = balance after t years, r = interest rate expresses as a decimal, n = number of compounding periods per years.

38. A deposit of $2500 invested into an account paying an interest rate of 10%. Find its balance after 5 years if interest is compounded… a.quarterly b. monthly c. continuously

39. A deposit of $2500 invested into an account paying an interest rate of 10%. Find its balance after 5 years if interest is compounded… a.quarterly b. monthly c. continuously