Math Log and E rules
When given values and an equation tl plug knto
-expand given completely -make sure values given are present in expanded equation -plug in values -solve
When the rquation has the same log or ln
-simplify/condense COMPLETELY -take away log/ln -solve
ln1
0
logb of 1
0
Logb of b
1
lne
1
e
2.72
Decreasing/increasing exponential function
A(t)=a(1+/-r)^t
How to find a function's equation using two points **
A) set up a system of equations using exponential equations B) divide two equations to eliminate a value and solve for b C) plug b value into an og. Equation to fimd a value D) rewrite functions equation using values found for a and b
Compound interest formula
A=P(1+r/n)^nt
Compound continuously formula
A=Pe^rt
Variable in the exponent
Find common base, if bases are different, see if you can make the larger one a power of the smaller one.
When 0<b<1
Graph is decreasing
When b>1
Graph is increasing
Solving exponential equations using a common base
If they do not have a common base, tale the log! -isolate the variable -able to take "log" because the log have the same value -exponents go before log -can use this with natural log***
Horizontal asymptotes
Occur usually at lowest point of graph
How to find y intercept if vert shifts
Plug in 0 for x
Fractional base and variable exponent
Use a negative exponent when rewriting with the common base
Log b of b^x
X
b^logb of x
X
e^knx
X
lne^x
X
"A" value in exponential function
Y-intercept, when no additional vert shifts
Standard form of an exponential function
Y=a(b)^x
Logarithm
Y=log base 2 of x, 2^y=x