APPLICATIONS OF EXPONENTIAL|
AND|
LOGARITHMIC FUNCTIONS|

EARTHQUAKE WORD PROBLEMS:

As with any word problem, the trick is convert a narrative statement or question to a mathematical statement.

Before we start, let's talk about earthquakes and how we measure their intensity.

In 1935 Charles Richter defined the magnitude of an earthquake to be

where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a ''standard earthquake'' (whose amplitude is 1 micron =10-4 cm).

The magnitude of a standard earthquake is

Richter studied many earthquakes that occurred between 1900 and 1950. The largest had magnitude of 8.9 on the Richter scale, and the smallest had magnitude 0. This corresponds to a ratio of intensities of 800,000,000, so the Richter scale provides more manageable numbers to work with.

Each number increase on the Richter scale indicates an intensity ten times stronger. For example, an earthquake of magnitude 6 is ten times stronger than an earthquake of magnitude 5. An earthquake of magnitude 7 is times strong than an earthquake of magnitude 5. An earthquake of magnitude 8 is times stronger than an earthquake of magnitude 5.

Example 1: Early in the century the earthquake in San Francisco registered 8.3 on the Richter scale. In the same year, another earthquake was recorded in South America that was four time stronger. What was the magnitude of the earthquake in South American?

Solution: Convert the first sentence to an equivalent mathematical sentence or equation.

Convert the second sentence to an equivalent mathematical sentence or equation.

Solve for MSA.

The intensity of the earthquake in South America was 8.9 on the Richter scale.

Example 2: A recent earthquake in San Francisco measured 7.1 on the Richter scale. How many times more intense was the San Francisco earthquake described in...

...MATH133 Unit 5: Exponential and LogarithmicFunctions
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to
type mathematics using the keyboard symbols.
IMPORTANT: See Question 1 in Problem 2 below for special IP instructions. This is
mandatory.
Problem 1: Photic Zone
Light entering water in a pond, lake, sea, or ocean will be absorbed or scattered by the particles
in...

...EXPONENTIAL AND LOGARITHMICFUNCTIONS
I.EXPONENTIAL FUNCTION
A. Definition
An exponentialfunction is a function defined by f(x) = ax , where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers.
B. Evaluating ExponentialFunctions
1. Given: f(x) = 2x, find
a. f(3) = ____ b....

...A function is a relation in which each element of the domain is paired with exactly one element in the range. Two types of functions are the exponentialfunctions and the logarithmicfunctions. Exponentialfunctions are the functions in the form of y = ax, where ''a'' is a positive real number, greater than zero and not equal to one. Logarithmic...

...Exponential and LogarithmicFunctions
* Verify that the natural logarithm function defined as an integral has the same properties as the natural logarithm function earlier defined as the inverse of the natural exponentialfunction.
Integrals of Exponential and LogarithmicFunctionsFunction | Integral |
lnx | x ∙ lnx - x + c |...

...LOGARITHMIC AND EXPONENTIALFUNCTIONS
Inverse relations
ExponentialfunctionsExponential and logarithmic equations
One logarithm
THE LOGARITHMICFUNCTION WITH BASE b is the function
y = logb x.
b is normally a number greater than 1 (although it need only be greater than 0 and not equal to 1). The function is defined for all...

...Solving Exponential and Logarithmic Equations
Exponential Equations (variable in exponent position)
1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e”...

...Practice Test
Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Tell whether the function y = 2( 5 ) shows growth or decay. Then graph the function. a. This is an exponential growth function. c. This is an exponential decay function.
x
b. This is an exponential growth function. d. This is an exponential growth...

...In mathematics, the exponentialfunction is the function ex, where e is the number (approximately 2.718281828) such that the function ex is its own derivative.[1][2] The exponentialfunction is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is...