for the unit test (Exponents and logarithms)

Today I will write about review that we should remember from EXPONENTS & LOGARITHMS.


1. You need to know the Y=2^x,.Y=2^-x, and Y=log2^X(X=2^Y) graphes
and how this things are effect to the graphes
Ex) differents between Y=3^X(narrow) and Y=2^X(wide)
differents between Y=-2^X(the graph looked like flip over the Y=2^X) and Y=2^X
differents between Y=2^(x-1) and Y=2^x-1
differents between Y=log2^x and Y=2^x this is inverse releation

X Y X Y
1 0 0 1
2 1 1 2
4 2 2 4
1/2 -1 -1 1/2
1/4 -2 -2 1/4

2.Logarithmic Function
Y=log2X = X=2^y

Ex) 4=log5625 = 625=5^4

3. know the formulas
loga(MN)=logaM=logaN
loga(M/N)=logaM-logaN
loga(M^n)=nlogaM
logaM=logbM/logba
when the base is 10, we can use our calculator to evaluate!

4. Logarithm
ln=log(e)
ln(e)=1

5. Applications of the exponential function
compound interest
A=P(1+r/n)^nt

where: P=principal amount (amount invested, or what you start out with)
r=rate of interest (always change to a decimal when substituting into the equation)
n=the number of times/year interest is to be calculated
t=the time in Years

Continuous Compound Interest
A=Pe^rt

Where: A=final amount
P=principal amount (amount invested, or what you start out with)
r=rate of interest (always change to a decimal when substituting into the equation!)
t=the time
e=2.718......


Continuous Growth or Decay
A=A0e^kt = A=Pe^rt