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Welcome back!Crunch time is on! 6 more classes to prepare for your diploma!
What do you need to know?
Review time is essential outside of the classroom
Bring in $10 for your KEY.
In Class Exam will be Wednesday, January 18th> This will replace your lowest unit exam
Your last day to hand in missing assignments is Thursday, January 12th.
If you want to rewrite your probability exam, you need to schedule it on your own time. Please confirm with me ahead of time.
Diploma is Wednesday, January 25th at 9:00. YOU CANNOT BE LATE.
Diploma Review Exponential Functions
Relations and Functions: weighting 50% (about 20 questions)
This includes Rational Expressions, Exponential Functions, Log Functions, Polynomial Functions, Sinusoidal Functions.
Diploma Review Logarithmic Functions
Relations and Functions: weighting 50% (about 20 questions)
This includes Rational Expressions, Exponential Functions, Log Functions, Polynomial Functions, Sinusoidal Functions.
Generally, an exponential function is in the form
where ''a"' represents the initial value ''b"' represents the rate of change
a can not equal zerob can not equal one
a) domainb) rangec) x interceptd) y intercepte) end behaviorf) asymptote
Example 1
For the graph of
a) domain
b) range
c) x intercept
d) y intercept
e) asymptote
f) calculator ..if you have the old system how can you enter this?
g) end behavior
h) Algebraically determine and graph the inverse function.
Example 2
Remember:To get the inverse we interchange the x and y values in an equation.
E.g.
Solving Equations
When x is the base, cancel out the exponent by using the reciprocal power.Isolate x first.
Example 1 Solve for x.
a)
b)When x is the exponent, write with a common base and eliminate the bases.Isolate the power first.
c)
d) Use logs to solve these ones
e) Solve this one algebraically
Example 2
a ) b)
Example 3 Change to log form.
b)
c)
a)
ln x = 2 f)
Example 4 Solve, to the nearest hundredth, where applicable.
*solve graphically
Example 5
If
find the value of k to the nearest whole number.
and
Properties of Logs
.
Example 1
Use the laws of logarithms to simplify to a single logarithm
The expression is equivalent to
A.
B.
C.
D.
Example 2
Word Problems
The population is given by where y is the population size and x is the number of years.
a) What does the 1500 represent?
b) What is the rate of growth?
c) Predict the population in 10 years
d) When in the population at 10000?
Example 1
Example 2
Compound Interest
A....accumulated amount (end amount)P... initial value (start amount)i..... interest per period
(annual rate divided by compounding factor)n... number of compounding periods
(years times the compounding factor)
Compounding factors: annually 1semiannually 2quarterly 4monthly 12
Ex: 1500 is invested at 3% compounded semiannually for 5 years. Determine the end balance
Half Life Problems
Caffeine has a half life of 8 hours. How long will it takefor 370 mg to decay to 80 mg?
Doubling, Tripling, etc...and
A population of butterflies double every two weeks. After 10 weeks there are 1920 butterflies. How many were there to start with?