Precalculus – MAT 129. Instructor: Rachel Graham Location: BETTS Rm. 107 Time: 8 – 11:20 a.m. MWF. Chapter Three. Exponential and Logarithmic Functions. Ch. 3 Overview. Exponential Fxns and Their Graphs Logarithmic Fxns and Their Graphs Properties of Logarithms
Instructor: Rachel Graham
Location: BETTS Rm. 107
Time: 8 – 11:20 a.m. MWF
Exponential and Logarithmic Functions
Pg. 187 Example 4
After looking at the solution read the paragraph at the bottom of the page.
Pg. 189 Example 6
Be sure you know how to evaluate this function on your calculator.
After t years, the balance A in an account with principal P and annual interest rate r (in decimal form) is given by the following formulas:
Pg. 191 Examples 8 and 9.
You will be responsible for knowing the compound interest formula.
1. Determine the balance A at the end of 20 years if $1500 is invested at 6.5% interest and the interest is compounded (a) quarterly and (b) continuously.
2. Determine the amount of money that should be invested at 9% interest, compounded monthly, to produce a final balance of $30,000 in 15 years.
For x>0, a>0, and a≠1,
y=logax if and only if x=ay.
f(x)=logax is called the logarithmic function with base a.
Pg. 203 #33.
Solve the equation for x.
Pg. 203 #33.
y=ln x if and only if x=ey.
f(x) = logex = ln x is called the natural logarithmic function.
Pg. 201 Example 9.
Note both the algebraic and graphical solutions.
See example 10 on pg. 202 for the best application of logarithmic functions.
To evaluate logarithms at different bases you can use the change of base formula:
logax = (logbx/ logba)
Pg. 207 Examples 1 & 2.
Note both log and ln functions will yield the same result.
See blue box on pg. 208.
Pg. 208 Example 3
These should be pretty self explanatory.
Pg. 209 Examples 5&6.
Note that a square root is equal to the power of ½.
In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After 2 days there are 100 fruit flies, and after 4 days there are 300 fruit flies. How many flies will there be after 5 days?
On a college campus of 5000 students, one student returns from vacation with a contagious flu virus. The spread of the virus is modeled on pg. 230 where y is the total number infected after t days. The college will cancel classes when 40% or more are infected.
R = log10 I/I0
where I0 = 1 is the minimum intensity used for comparison. Intensity is a measure of wave energy of an earthquake.
In Class QUIZ:
#30, 41a, 42a.