7. Supply of a product increases according to the model S(p) = a In(p – b) thousand units per week at a price of p dollars per unit. Suppliers are first willing to provide the product when it is priced at 10 dollars per unit (in the sense that when p = 10, S(p) = 0). When charging 20 dollars per item, suppliers provide 3 thousand items per week. (a) Find the value of constants a and b in the supply function formula. (b) What is the mathematical domain of S? Is this different from the practical domain of S?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.