1. Warm-up (8 min.) Expand 1) ln 8x 2) log 1000x4 Simplify
3) 2ln x + 3ln y 4) 3 log x + log y – 2 log z
Use change-of-base formula to evaluate
5) log9 27

2. Equation solving, modeling, and finance
Sections

3. One-to-One Properties
Yet another property:
One-to-One Properties
If then
If then

4. Ex.
a) c)
b) d)

5. Real life applications
The Richter scale measures the magnitude, R, by the formula
a is the micrometers of vertical ground motion
T is the period of the associated seismic wave in seconds
B accounts for the weakening of the seismic wave with increasing distance form the epicenter of the earthquake.

6. Comparing Earthquakes
How many times more severe was the 1995 Kobe, Japan earthquake (R=7.2) than the 1994 Los Angeles earthquake (R=6.6).

7. Real life applications
Newton’s Law of Cooling
= the temperature of the surrounding medium
= initial temperature of the object

8. Math of Finance Compound interest:
A = value of investment after time, t, in years.
P = principal amount invested
r = fixed annual interest rate
k = amount the interest is compounded per year

9. “Interest”-ing
I put 500 dollars in an account for 5 years that earns 4% compounded monthly.
Identify the variables in compound interest formula
Solve the formula for the amount of money that you would have at the end of the 5 years

10. Your try…
You invest 650 in a bank account your freshman year of high school. Four years later, after graduation, you want to take your investment and put a down payment on a car. The account compounds the interest quarterly, at a rate of 3.5%. How much is the down payment that you will make?

11. Interest Compounded Annually
What is the formula for interest compounded annually?

12. Interest compounded Continuously
What is the formula for interest compounded continuously?

13. example
Slammin’ Sammy deposited 450 dollars in an account that was compounded continuously at a 2.75% for 10 years. How much did he have at the end of the ten years?

14. Homeworkage… Pg 331 #’s 1-9 odd, 19-24, 25, 32, 37, 45, 49 Pg 342