Example 5: Change of Price Vector

In economics the price vector may change with time and thus be a vector valued function of t. Find the price vector function P(t) for three commodities such that the first commodity has price t², the second has price t + 1, and the price of the third commodity is the sum of the other two (f ≥ 0). The answer is

P(t) = t²i + (t + 1)j + (t² + t + 1)k.