The quantity M varies directly as x and inversely as y if x

The quantity M varies directly as x and inversely as y if x= 3 and y = 14, then M = 4 ..Write M as a function of x and Y. A company has found that the demand for its product varies inversely as the price of the product. when the price x is 4 dollars, the demand y is 400 units. Find a mathematical model that gives the demand y in terms of the price x in dollars. Approximate the demand when the price is 9.5 dollars.

Solution

Problem 12:

given that M is directly proportional to x

M = k1*x

M is inversely proportional to y

M = k2/y

which gives us

M = kx/y, where k = k1*k2

Now given that when x = 3 & y = 14, then M = 4

4 = 3*k/14

k = 56/3

So function will be:

M = 56*x/(3*y)