blog #7

This week we learned about solving related rate word problems.
There are a set of steps to follow when solving a related rate problem but first you need to know how to recognize a related rate problem.
A related rate problem is one that involves something per something.
I.E. Gallons per minute
Cubic feet per second
Your key word is PER
Keep in mind that although there are set steps for working related rate problems but each problem is unique in its own method of solution.
To further explain the steps are guidelines but the specific application is dependent upon each problem.
The steps to solving these problems are as follows.
First, identify all given quantities and quantities to be determined. Also make a sketch and be sure to label the quantities.
Second, you must write an equation involving the variables whose rates of change either are given or are to be determined
Third, you must use the chain rule implicitly differentiate both sides of the equation with respect to time (T)
Finally, you must substitute all known variables into the resulting equation and solve for the desired rate of change
Be sure to print and study your Geometric formulas
Example:
A Pebble is dropped into a calm pond causing ripples in the form of concentric circles. The radius of the outer circle is increasing at a rate of 1 foot PER second when the radius is 4 ft at what rate is the total area (A) of the disturbed water changing?
#1 dr/dt= 1ft/sec
R=4 ft
dA/dt= ?
#2 A= pi r ^2
#3 dA/dt= pi{2r dr/dt}
#4 dA/dt= 2pi (4)(1)
Therefore 8 pi ft/sec