4 types of variation Direct Variation Use this when we read “varies directly” or “directly proportional.” The basic model is based on the equation: y.

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Presentation transcript:

4 types of variation

Direct Variation Use this when we read “varies directly” or “directly proportional.” The basic model is based on the equation: y = kx Where k is the constant of variation

Example of direct variation The simple interest on an investment is directly proportional to the amount of the investment. By investing $2500 in a certain bond, you obtained an interest payment of $87.50 after 1 year. Find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P.

Solution I = Prt(set up initial formula) = 2500(r)1 (substitute values we know).035 = r(solve for the missing value) I = P(.035) or I =.035P Now go back to the original formula and substitute your finding. You just calculated the “k” value and created a linear model to calculate any interest earned given the principle.

Inverse Variation Use this when we read “varies inversely” or “inversely proportional.” The basic model is based on the equation: y = Where k is some constant.

Example of Inverse Variation A company has found that the daily demand y for its boxes of chocolates is inversely proportional to the price p. When the price is $5, the demand is 800 boxes. Approximate the demand when the price is increased to $6.

Solution Because this varies inversely, we start with the equation y =. Adding the information we know: 800 = k = 4000 Applying that k-value: y = y = 666

Varies Jointly The work W (in joules) done when lifting an object varies jointly with the mass m (in Kg) of the object and the height h (in meters)that the object is lifted. The work done when a 120-Kg object is lifted 1.8 meters is joules. How much work is done when lifting a 100-Kg object 1.5 meters?

W = mhk = 120(1.8)k = 216k K = 9.8 Apply the k-value W = 100(1.5)(9.8) = 1470 joules

One more The diameter of the largest particle that can be moved by a stream varies directly as the square of the velocity of the stream. The velocity of a stream moving.25 mph can move a particle.02 inches in diameter. What velocity is required to carry particles.12 inches in diameter?

Solution y = kx 2.02 = k(.25) 2.02 =.0625k k =.32 Apply the k-value.12 =.32x = x 2 x =.612 mph