Questions from General Calculus

Q: Find the logarithmic derivative and then determine the percentage rate of change

Find the logarithmic derivative and then determine the percentage rate of change of the function at the point indicated. f (t) = t10 at t = 10 and t = 50

Q: An electronic store can sell q = 10,000/(p

An electronic store can sell q = 10,000/(p + 50) - 30 cellular phones at a price p dollars per phone. The current price is $150. (a) Is demand elastic or inelastic at p = 150? (b) If the price is lowe...

Q: A movie theater has a seating capacity of 3000 people. The

A movie theater has a seating capacity of 3000 people. The number of people attending a show at price p dollars per ticket is q = (18,000/p) - 1500. Currently, the price is $6 per ticket. (a) Is deman...

Q: Suppose that the function P(t) satisfies the differential equation

Suppose that the function P(t) satisfies the differential equation y’(t) = -.5y(t), y(0) = 10. (a) Find an equation of the tangent line to the graph of y = P(t) at t = 0. (b) Find P(t). (c) What i...

Q: A subway charges 65 cents per person and has 10,000

A subway charges 65 cents per person and has 10,000 riders each day. The demand function for the subway is q = 2000 √(90 – p). (a) Is demand elastic or inelastic at p = 65? (b) Should the price of a r...

Q: A country that is the major supplier of a certain commodity wishes

A country that is the major supplier of a certain commodity wishes to improve its balance-of-trade position by lowering the price of the commodity. The demand function is q = 1000/p2. (a) Compute E(p)...

Q: Show that any demand function of the form q = a/

Show that any demand function of the form q = a/pm has constant elasticity m.

Q: A cost function C(x) gives the total cost of

A cost function C(x) gives the total cost of producing x units of a product. The elasticity of cost at quantity x, Ec (x), is defined to be the ratio of the relative rate of change of cost (with respe...

Q: A cost function C(x) gives the total cost of

A cost function C(x) gives the total cost of producing x units of a product. The elasticity of cost at quantity x, Ec (x), is defined to be the ratio of the relative rate of change of cost (with respe...

Q: A cost function C(x) gives the total cost of

A cost function C(x) gives the total cost of producing x units of a product. The elasticity of cost at quantity x, Ec (x), is defined to be the ratio of the relative rate of change of cost (with respe...