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Level 399

Logarithmic/Exponential Functions


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a*a*a... x times.
a^x=; x is a positive integer...
1/(a^x)
a^-x; x is a positive integer...
a^(x+4)
a^x * a^4=
(a^x)/(a^4)=
a^(x-4)
(a^x)^4=
a^(x4)
a^0=
1
x=Power; y=Root
a^(x/y); x=?, y=?
n√a^m = (n√a)^m
Radical form for... a^(m/n)
|x|
n√x^n=; Where n is even...
x
n√x^n=; Where n is odd...
Scientific Notation: The General Rule...
? . ? ? ...x10^? = the original number.
=(1+(1/x))^x; x→∞
e= (Two expressions)
2.718
e is approximately...
f(x)=b^x; b>1
Horizontal Asymptote: y=0
f(x)=b^x; -<b<1
Horizontal Asymptote: y=0
f(x)=e^x
(Steeper Exponential Growth)
log↓a(xy)=
log↓a(x)+log↓a(y)
log↓a(x/y)=
log↓a(x)-log↓a(y)
log↓a(x)^4=
ylog↓a(x)
(logb)/(loga)=lnb/lna
Change of Base... log↓a(b)
ln1=
0
lne=
1
f(x)=log↓b(x); b>1
(Exponential Decay flipped over x-axis)
f(x)=log↓b(x); 0<b<1
(Exponential Growth flipped over x-axis)
f(x)=lnx
(Exponential Decay flipped over x-axis)
Investment total under simple interest; A=...
A=P(1=rt); P=Principle, r=Interest Rate (Decimal Percentage), t=Number of years.
Investment total under compound interest; A=...
A=p(1+(r/m))^mt; m=Number of times compounded per year.
A=Pe^(rt)
Investment total under continuously compounded interest; A=...
y=Be^(kt); k>0
Population Growth Model; y=?
y=Be^(kt); k<0
Radioactive Decay Model; y=?
y=A-Be^-(kt); t≥0
Bounded Growth Learning Curve; y=?
y=(A)/(1+(Be^-(Akt)); t≥0
Logistic Growth; y=?