Example #1 (Sound Intensity): The relationship between the number of decibels B and the intensity of a sound I in watts per centimeter squared is given by:
Determine the intensity of a sound I if it registers 125 decibels on a decibel meter.
In examples #2 and 3, compare the intensities of the two earthquakes.
2.
| Location | Date | Magnitude |
|---|---|---|
| San Francisco, CA | 4/18/1906 | 8.3 |
| Napa, CA | 9/3/2000 | 4.9 |
Formula: R = log10I, where I is the intensity of the shockwave and R is the magnitude of an earthquake.
3.
| Location | Date | Magnitude |
|---|---|---|
| El Salvador | 2/13/2001 | 6.5 |
| Columbia | 1/25/1999 | 5.7 |
Example #4 (Human Memory Model): The average score A for a group of students who took a test t months after the completion of a course is given by the human memory model:
A = 80 - log10(t + 1)12
How long after completing the course will the average score fall to A = 72?
Example #5 (Newton's Law of Cooling): You place a tray of water at 60oF in a freezer that is set at 60°F. The water cools according to Newton's Law of Cooling:
a) The water freezes in 4 hours. What is the constant k? (Hint: Water freezes at 32°F.)
b) You lower the temperature in the freezer to -10°F. At this temperature, how long will it take for the ice cubes to form?
c) The initial temperature of the water is 50°F. The freezer temperature is 0°F. How long will it take for the ice cubes to form?
