Exercise 4.3.24 The supply function for a certain make of transistor radio is given by p = f(x) = 0.00001x5/4 + 10 where x is the quantity supplied and p is the unit price in dollars. (a) Find f'(x). (b) What is the rate of change of the unit price if the quantity supplied is 10,000 radios? Exercise 4.3.22 An economy's consumer price index (CPI) is described by the function I(1) = -0.273+3+2+ 100 0 St S 10 where t = 0 corresponds to 1994. (a) At what rate was the CPI changing in 1999? In 2001? In 2004? (b) What was the average rate of increase in the CPI over the period from 1999 to 2004? Exercise 4.3.28 The total revenue in dollars for a video game is given by R(x) = To0 (x + 2000) (1600 -x) - 36,000 where x is the number of units sold. What is the rate of change of revenue with respect to x when 600 units are sold? Interpret your result. Exercise 4.4.13 The number of viewers of a television series introduced several years ago is approximated by the function N(x) = (60+2x)2/3 15x5 26 where N(x) (measured in thousands) denotes the number of weekly viewers of the series in the x-th week. Find the rate of increase of the weekly audience at the end of week 2 and at the end of week 12. How many viewers were there in week 2? In week 24? Exercise 4.4.16 Government economists of a developing country determined that the purchase of im- ported perfume is related to a proposed "luxury tax" by the formula N(x) = V10,000 -40x - 0.02x2 0x 200 where N(x) measured the percentage of normal consumption of perfume when a "luxury tax" of x is imposed on it. Find the rate of change of N(x) for taxes of 10, 100, and 150 %