Zusammenfassung der Ressource
Chapter 3 & 4
- Chpt. 3 Sect 1
Anmerkungen:
- exponential decay and growth
- Exponential growth
- f(x)=Ca^x
Anmerkungen:
- X= time
a= Growth factor
C= initial value
- Exponential decay
- 0<a<1
- a>1
- Chpt. 3 Sect 2
Anmerkungen:
- Exponential Models: Comparing Rates
- Annual Percentage rate
- (1+ r/n)^n*1
Anmerkungen:
- r= rate
n=time
Annually= 1
Semi-annually= 2
Quarterly= 4
Monthly= 12
Weekly= 52
Daily=365
- Compound Interest
- P(1+r/n)^n*t
- Chpt. 3 Sect
3
- Average rate of change
- f(b)-f(a)/b-a
- percentage rate of change
- f(x+1)-f(x)/f(x)
- Chpt. 3 Sect 4
Anmerkungen:
- Graphs of Exponential Functions
- exponential function with a base
- f(x)=a^2
- a>0 & a=1
- Chpt. 4 Sect. 1
Anmerkungen:
- Logarithmic base 10
- log10 X=Y
Anmerkungen:
- Powers of 10
Anmerkungen:
- 10^-4= -4
10^-3=-3
10^-2=-2
10^-1=-1
10^0=0
10^1=1
10^2=2
10^3=3
10^4=4
- logarithm base
- loga x=y
- log function w base
- f(x)= loga X
- Basic properties of logarithms
Anmerkungen:
- loga 1=0
loga a=1
loga a^x=x
a^logax =x
- Chpt. 4 Sect 2
Anmerkungen:
- Laws of logarithms
Anmerkungen:
- lawa AB= loga A+ loga B
loga A/B= logaA - loga B
loga Ac = ClogaA
- log(12/n)
- log12-logn
- change of base formula
Anmerkungen:
- Chpt. 4 Sect 3
Anmerkungen:
- Linear Scale
Anmerkungen:
- fixed marks on the scale corresponds to an adding a fixed constant.
- log scale
Anmerkungen:
- each mark on the scale corresponds to multiplying by a fixed factor.
- pH scale
- pH less than 7 is acidic
- pH greater than 7
is basic
- 7 is neutral
- The Decibel Scale
Anmerkungen:
- S= k*log(l/lo)
Io=10-12W/m2
B=10*log (I/Io)
- Richter
Scale
Anmerkungen:
- Chpt.4 Sect 4
Anmerkungen:
- Natural Exponential and Logarithmic Functions
- natural logarithm function
Anmerkungen:
- natural exponential function
Anmerkungen:
- compounded continously
Anmerkungen:
- 25000(1+0.06/4)^(4*10)
Anmerkungen:
- $25000 is invested at a rate of 6% per year, invested in 10 years and is compounded quarterly
- $45350.46
- Chpt. 4 Sect 5
Anmerkungen:
- 2^x=16
- log2^2x=log2^16
- x=log2^2^4
- x=4