Unit 7 Exponential and Logarithmic Functions

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Unit 7 Exponential and Logarithmic Functions by Mind Map: Unit 7 Exponential and Logarithmic Functions

1. Lesson 1 Exponential function

1.1. b>1

1.2. y=2^x

1.3. b=2

1.4. a=1

1.5. Growth

1.5.1. Increasing

1.6. Parent function

1.6.1. a*b^x

1.7. Domain

1.7.1. Inequality

1.7.1.1. -∞<x<∞

1.7.2. Interval

1.7.2.1. (-∞,∞)

1.8. Range

1.8.1. (0,∞)

1.9. Horizontal Asymptote

1.9.1. y=0

1.10. Compression

1.11. Vertical Asymptote

1.11.1. None

1.12. Y-int

1.12.1. (0,1)

1.13. End Behaviors

1.13.1. Right

1.13.1.1. X→+∞

1.13.1.2. Y→0

1.13.2. Left

1.13.2.1. x→+∞

1.13.2.2. Y→∞

2. y=a*b^x

2.1. L1: -6,-2,0,3,4

2.2. L2: .13, .99, 2.89, 13.9, 23.9

2.3. y=2.91(1.69)^x

2.3.1. y=193.64

2.4. x=8

3. y=b^x

3.1. 7^2=49

4. x=logbY

4.1. log81(9)=1/2

5. The compound interest formula is P=A(1+i)^n, where A is the original value of an investment, i is the interest rate per compounding period, n is the total number of compounding periods, and P is the value of the investment after n compounding periods. An investor deposits $2500 into an account which earns 9% annual interest compounded semi- annually. In approximately how many years will the investment be worth twice the original amount?

5.1. A=2500

5.2. i=9% or .9

5.3. 2n

5.4. p=2500(1+.09)q2r5

6. b>1