Section 3.5 – Mathematical Modeling

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Presentation transcript:

Section 3.5 – Mathematical Modeling

Direct Variation - Inverse Variation - x 2 4 6 8 10 8 32 72 128 200 1 4 9 16 25

Direct Variation - Inverse Variation - x 2 4 6 8 10 5/4 5/16 5/36 5/64 1/20 5 5/4 5/9 5/16 1/50

Direct Variation - OR Inverse Variation - YES NO DIRECT VARIATION

Direct Variation - OR Inverse Variation - NO YES INVERSE VARIATION

Direct Variation - Inverse Variation - Directly Proportional - If x = 2 and y = 14, write a linear model that relates y to x if y is directly proportional to x. If x = 6 and y = 580, write a linear model that relates y to x if y is directly proportional to x.

The simple interest (I) on an investment is directly proportional to the amount of the investment (P). By investing $5000 in a municipal bond, you obtained an interest payment of $187.50 after one year. Find a mathematical model that gives the interest (I) for this municipal bond after one year in terms of the amount invested (P).

The distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 220 newtons stretches a spring 0.12 meters. What force is required to stretch the spring 0.16 meters?

Direct Variation - Inverse Variation - Directly Proportional - Write a mathematical model for each of the following: A) y varies directly as the cube of x B) h varies inversely as the square root of s C) c is jointly proportional to the square of x and

Write a mathematical model for each of the following. In each case, determine the constant of proportionality. A) y varies directly as the cube of x. (y = 81 when x = 3) B) h varies inversely as the square root of s. (h = 2 when s = 4) C) c is jointly proportional to the square of x and (c = 144 when x = 3 and y = 2)

Direct Variation - Inverse Variation - Directly Proportional - The stopping distance d of an automobile is directly proportional to the square of its speed s. A car required 75 feet to stop when its speed was 30 mph. Estimate the stopping distance if the brakes are applied when the car is traveling at 50 mph.