# A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.5 dollars, the demand y is 400 units. How do you find a mathematical model that gives the demand y in terms of the price x in dollars?

Apr 5, 2016

Mathematical model equation for demand of company's product is given by the equation $d = \frac{1800}{p}$.

#### Explanation:

Let demand for company's product $d$ vary inversely with its price $p$, which means

$\mathrm{dp} r o p \left(\frac{1}{p}\right)$ or $d = k \times \left(\frac{1}{p}\right) = \frac{k}{p}$.......(A)

As when $p = 4.5$, $d = 400$

Putting these in (A), we get $400 = \frac{k}{4.5}$

Hence #k=400xx4.5=1800 and our model equation is

$d = \frac{1800}{p}$