1 / 18

MATH!

MATH!. by: Donna Ball and Pam. 5.2 Exponential Functions & Graphs. F(x)=a x x= real # a>0, a 1 Graphing Basics Base e: f(x)=e x , g (x)=e -x Compound Interest: A=P(1+ (r/n)) nt P=initial value, r=rate, n=amount compounded annually, t=time. Ch . 5.2 Example.

Download Presentation

MATH!

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. MATH! by: Donna Ball and Pam

  2. 5.2 Exponential Functions & Graphs • F(x)=ax • x= real # • a>0, a 1 • Graphing Basics • Base e: • f(x)=ex, g(x)=e-x • Compound Interest: • A=P(1+ (r/n))nt • P=initial value, r=rate, n=amount compounded annually, t=time

  3. Ch. 5.2 Example

  4. 5.3 Logarithmic Functions & Graphs • Log Function Equation: • y=logax • x>0 • a=positive #, a 1 • General Rules: • loga1=0, ln1=0 • logaa=1, lne=1 • Log to Exponential: • logax=yx=ay • Change of Base: • logbM=(logaM/logab)

  5. Ch. 5.3 Example

  6. 5.4 Properties of Logarithmic Functions • Product Rule: • logaMN=logaM+logaN • Power Rule: • logaMp=plogaM • Quotient Rule: • loga(M/N)=logaM-logaN • Logarithm of a Base to a Power: • logaax=x • Base to a Logarthimic Power: • Alogax=x

  7. Ch. 5.4 Example

  8. 5.5 Solving Exponential & Logarithmic Equations • Base-Exponent Property: • ax=ayx=y • a>0, a (can't)=1 • Property of Logarithmic Equality: • logaM=logaNM=N • M>0, N>0, a>0, a (can't)=1

  9. Ch. 5.5 Example

  10. 5.6 Growth, Decay, & Compound Interest • Growth Equation: • P(t)=Poekt • k>0 • Growth Rate & Doubling Time: • KT=ln2 • K=(ln2/T) • T=(ln2/K) • Exponential Decay: • P(t)=Poe-kt • k>0 • Decay Rate & Half Life: • KT=ln2 • K=(ln2/T) • T=(ln2/K)

  11. Ch. 5.6 Example

  12. Ch. 5.6 Example (continued)

  13. 7.1 Pythagorean and Sum and Difference • Basic Identities: • Pythagorean Identities: • Sum & Difference Identities:

  14. Ch. 7.1 Example

  15. 7.2 Cofunctions, Double-Angle, & Half-Angle • Cofunction Identities: • Double-Angle Identities: • Half-Angle Identities:

  16. Ch. 7.2 Example (cofunctions)

  17. 7.3 Proving Trigonometric Identities • Method 1: • Start with one side and solve for opposite side. • Method 2: • Solve both sides until they're equal to each other. • Product-to-Sum Identities: • Sum-to-Product Identities:

  18. Ch. 7.3 Example

More Related