Final answer:
The mathematical model that reflects the inverse relationship between price and demand, as per the law of demand, is D = 1400/P, found by using the given values of price and demand.
Step-by-step explanation:
The student is asking for a mathematical model that describes the inverse relationship between the price of a product and the quantity demanded for that product.
This relationship is explained by the law of demand, which states that, ceteris paribus, as the price of a product increases, the quantity demanded decreases, and vice versa.
To find this mathematical model, we can use the information provided: when the price is $3.5, the demand is 400 units.
We can express this inverse relationship with the formula D = k/P, where D is demand, P is price, and k is a constant. Substituting the given values, we find that k = D × P
= 400 × 3.5
= 1400.
Therefore, the model that gives the demand in terms of price is D = 1400/P.