2. 4 types of variation

3. 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

4. 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.

5. Solution I = Prt(set up initial formula) 87.50 = 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.

6. 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.

7. 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.

8. 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

9. 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 2116.8 joules. How much work is done when lifting a 100-Kg object 1.5 meters?

10. W = mhk 2116.8 = 120(1.8)k 2116.8 = 216k K = 9.8 Apply the k-value W = 100(1.5)(9.8) = 1470 joules

11. 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?

12. Solution y = kx 2.02 = k(.25) 2.02 =.0625k k =.32 Apply the k-value.12 =.32x 2.375 = x 2 x =.612 mph