1. xy -21/16 1/4 01 14 216 xy -25/4 5/2 05 110 220 xy -22/9 2/3 02 16 218 xy -29 3 01 11/3 21/9 xy -28 4 02 11 21/2 xy -216 8 04 12 21 1. 2. 3. 4. 5. 6. 7. a) growth b) (0.3)8. a) growth b) (0,4)9. a) decay b) (0,5) 10. a) decay b) (0,.5)11. a) growth b) (0,10)12. a) decay b) (0,1) 13. a) decay b) (0,2) 14. a) growth b) (0,1/2)15. a) growth b) (0,1) 16. $1,500(1+0.06) 5 = $2,007.3917. $300,000(1-0.2) 5 = $98,304 18. $75,00(1+0.125) 30 = $2,568,247.8719. $29,000(1-0.12) 7 = $11,851.59 20. $120,00(1+0.012) 5 = $127374.80 21. $1,860,000(1-0.035) 10 = $1,302,525.03

2. 7.2 – Properties of Exponential Functions & 7.3 – Logarithmic Functions as Inverses

3. Natural base exponential functions are exponential functions with base e. e ≈ 2.71828 These functions are used in order to describe continuous growth or decay.

4. Continuously Compounded Interest A(t) = P  e (r)(t) Interest Rate (annual) Time in years Principa l Amount in account at time t

5. Ex: Suppose your little brother won a contest at the start of 5 th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will he have when he starts high school four years later? (Express to the nearest dollar) t = r = P = A(t) =

6. Ex: Suppose you win $2000 in the lottery. If you deposit this money in an account that pays 5.1% interest, how much money will you have in 3 years? t = r = P = A(t) =

7. A logarithm base b of a positive number x satisfies the following definition: For b > 0, b ≠ 1, log b x = y if and only if b y = x log b x can be read as “log base b of x” y is the exponent to which base b must be raised to get x.

8. Ex: Write 100 = 10 2 in logarithmic form Ex: Write 81 = 3 4 in logarithmic form

9. Ex: What is the value of log 8 32 (without using a calculator)?

10. Ex: What is the value of log 4 32 (without using a calculator)?

11. A common logarithm is a logarithm with base 10. So instead of writing log 10 x, you can simply write log x A logarithmic function is the inverse of an exponential function. The graph shows y = 10 x and it’s inverse y = log x Note: (0, 1) and (1, 10) are on the graph of y = 10 x and (1, 0) and (10, 1) are on the graph of y = log x. 

12. The function y = e x has an inverse as well. That inverse is called the natural logarithmic function: y = log e x or y = ln x

13. Ex: Use the definition of a natural logarithm to write 54.598= e 4 in natural logarithmic form Ex: Use the definition of a natural logarithm to write 7.389 = e 2 in natural logarithmic form

14. Homework Worksheet questions 22 – 43