Exponential Functions
Logarithmic Functions
Laws of Logarithms
Exponential
&
Logarithmic Equations
&
Logarithmic Equations
Modeling with Exponential Functions
100
What is the base of
f(x) = ax
base = a
100
Write ay= x in logarithmic form.
loga(x)=y
100
True or False
loga(AB)= loga(A) x loga(B)
False
100
For all of x, ex is *blank* than/to zero?
greater than
100
Exponential Growth (Double Time) Formula
n(t)=n02t/a
200
Evaluate the function. Round to tenths place
f(4/3) = 3x
f(4/3) = 4.3
200
Solve using Change of Base formula. Round to tenths
f(x) = log4(7)
1.4
200
Evaluate.
log2(80) - log2(5)
log2(16)=4
200
ln(8+x)= 2
e2-8
200
Radioactive decay formula
m(t)=m0e-rt
300
What is the Compound Interest Formula?
300
Find the domain of the function
f(x) = ln(4 - x2)
Domain: (-2,2)
300
Expand.
ln (ab/c)
ln(a) + ln(b) - ln(c)
300
Find the solution.
154x-5 = 1/15
x=1
300
What does r equal in the radioactive decay formula?
-ln2/h
400
Find the annual percentage yield for an investment that earns interest at a rate of per year, compounded daily
6.183%
400
Evaluate.
ex+3- 4 = 2
ln(6) - 3
400
Combine.
4log(x) - 1/3log(x2+1) + 2log(x-1)
log (x4(x-1)2)/(x2+1)1/3
400
Solve.
4 + 3log(2x) = 16
x = 5000
400
Radium-221 has a half-life of 30 sec. How long will it take for 84% of a sample to decay?
79 seconds
500
Graph f(x) = (1/2)x + 3. What is the asymptote?
horizontal asymptote: y=3, as x approaches infinity f(x)= (1/2)x+ 3 approaches 3.
500
Evaluate.
ln(1/e3)
-3
500
Simplify with Change of Base. Round to tenth
log2(5) x log5(7)
2.8
500
Solve.
3xex + x2e2 = 0
x=0, x=-3
500
Solve exponential function for x.
log5(x) + log5(x + 1) = log5(20)
x=4