Derivatives - Business Applications
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1)With a yearly rate of 3 percent, prices are described as P = P0 (1.03)t, where P0 is the price in dollars when t = 0 and t is time in years. If P0 is 1.2, how fast are prices rising when t = 15?
2)The value of a car is falling 10 percent per year so that if C0 is the purchase price of the car in dollars, its value after t years is given by V(t) = C0(0.9)t. At what rate is its value falling when it is driven out of the showroom? How fast has the car depreciated after year 1?
3)The quantity, q, of a certain skateboard sold depends on the selling price, p, in dollars, so we write q=f(p). You are given that f(140)=15,000 anf f'(140)=-100.
What do f(140)=15000 and f'(140)=-100 tell you about the sales of the skateboards?
The total revenue, R, earned by the sale of the skateboards is given by R=pq. Find dR over dP by p=140.
What is the sign of dR over dp by p=140? If the skateboards sell at $140, what happens to revenue if the price is increased to $141?
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