2. A manufacturer determined that when the price of a new phone is $500, the demand...

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2. A manufacturer determined that when the price of a new phone is $500, the demand is 800, 000 handsets. For every $10 price increase, the demand drops by 2%. Suppose it costs $200 to produce a phone. (a) Find the demand function in the form q = Cek, where x is the number of $10 increases, and q is the demand. Hint: The differential equation for q(x) is = .02q (b) Find, using calculus, the price that maximizes the total profit. (c) If you used the linear approximation q=mx+b for the demand function instead of the exponential function, how much would be the error when the price is $520? 2. A manufacturer determined that when the price of a new phone is $500, the demand is 800, 000 handsets. For every $10 price increase, the demand drops by 2%. Suppose it costs $200 to produce a phone. (a) Find the demand function in the form q = Cek, where x is the number of $10 increases, and q is the demand. Hint: The differential equation for q(x) is = .02q (b) Find, using calculus, the price that maximizes the total profit. (c) If you used the linear approximation q=mx+b for the demand function instead of the exponential function, how much would be the error when the price is $520?