Download Math 112 Section 2

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Math 112
Section 2.8 Modeling using variation
Direct variation
y = kx (y varies directly as x) , k≠0
k is the constant of variation
Example 1
The volume of blood, B, in a person’s body varies directly as body weight W. A person who weighs
160 pounds has approximately 5 quarts of blood. Estimate the number of quarts of blood in a person
who weights 200 pounds.
Direct variation with powers
y = kxn(y varies directly as the nth power of x) , k≠0
Example 2
The distance, s, that a body falls from res varies directly as the quare of the time, t, of the fall. If
skydivers fall 66 feet in 2 seconds, how far will they fall in 4.5 seconds?
Inverse variation
(y varies inversely as x) , k≠0
Example 3
If temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of
the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12
pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new
pressure of the gas?
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Combined variation
Situations can combine a direct and inverse variation
(y varies directly as x and indirectly as z)
Example 4
The owners of Rollerblades Plus determine that the monthly sales, S, of its skates vary directly as its
advertising budget, A, and inversely as the price of the skates, P. When $60,000 is spent on
advertising and the price of the skates is $40, the monthly sales are 12,000 pairs of rollerblades.
1) Write an equation of variation that describes this situation
2) Determine monthly sales if the amount of the advertising budget is increased to $70,000.
Joint Variation
Situations can vary directly as the product of two or more variables
y = kxz (y varies jointly as x and z)
Example 5
The centrifugal force, C, of a body moving in a circle varies jointly with the radius of the circular
parth, r, and the body’s mass, m, and inversely with the square of the time, t, it takes to move about
one full circle. A 6 gram body moving in a circle with radius 100 centimeters at a rate of 1 revolution
in 2 seconds has a centrifugal force of 6000 dynes. Find the centrifugal force of an 18 gram body
moving in a circle with radius 100 centimeters at a rate of 1 revolutions in 3 seconds.