A coffee roasting company is considering changing the price of its coffee. Let q

Question

A coffee roasting company is considering changing the price of its coffee. Let q(p) be the amount of coffee (in pounds) that the company sells each month if it charges p dollars per pound. Suppose the company currently charges p0 dollars for a pound of coffee. You may assume that q is a strictly decreasing function, but do not assume that q is an exponential function.

Your answer to this problem may involve the functions q, q^-1, and the constant p0

(a) If the company raises the price of its coffee by $1 per pound, then it will sell 10% less coffee per month than it currently sells. Write an equation that expresses this fact

(b) Write a mathematical expression that it is equal to the price that the company would have to charge in order to sell twice as much coffee as it currently sells

(c) Write a formula for a function E(p) that gives the amount of coffee (in kilograms) that the company sells each month if it charges p euros per kilogram. Note that there are about 2.2 pounds in 1 kilgram, and 1 euro is about $1.32 ( as of September 3, 2013)

Explanation / Answer

(a) q(p+1) = 0.9*q(p)

(b) 2q( p0) = q ( p- x)

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