If $1200 is invested in an account that pays 5 % compounded annually, the total amount, A(t), in the account after t years is Upper A (t )equals 1200 (1.05 )Superscript t . a. Find the average rate of change per year of the total amount in the account for the first five years of the investment (from tequals 0 to tequals 5 ). b. Find the average rate of change per year of the total amount in the account for the second five years of the investment (from tequals 5 to tequals 10 ). c. Estimate the instantaneous rate of change for tequals 5.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a.what is the firm’s labor demand function? b.if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c.now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

In a small group, members have taken on the task roles of information giver, critic/analyzer, and recorder, and the maintenance roles of gatekeeper and follower. they need to fulfill one more role. which of the following would be most effective for their group dynamics? a dominator b coordinator c opinion seeker d harmonizer

Google started as one of many internet search engines, amazon started as an online book seller, and ebay began as a site where people could sell used personal items in auctions. these firms have grown to be so large and dominant that they are facing antitrust scrutiny from competition regulators in the us and elsewhere. did these online giants grow by fairly beating competition, or did they use unfair advantages? are there any clouds on the horizon for these firms -- could they face diseconomies of scale or diseconomies of scope as they continue to grow? if so, what factors may limit their continued growth?