The amount of money invested in a certain account increases according to the following function, where is the initial amount of the investment, and is the amount present at time (in years). After how many years will the initial investment be doubled? Do not round any intermediate computations, and round your answer to the nearest tenth.

Which of the following mechanisms would be most likely to motivate managers to act in the best interests of shareholders? a) decrease the use of restrictive covenants in bond agreements, b) take actions that reduce the possibility of a hostile takeover, c) elect a board of directors that allows managers greater freedom of action, d) increase the proportion of executive compensation that comes from stock options and reduce the proportion that is paid as cash salaries, e) eliminate a requirement that members of the board directors have a substantial investment in the firm's stocks

In return for their with optimizing his painting project, the castle servant informed poly and digit that he saw someone dressed as the king leaving behind a trail of crumbs as he walked into the jester's room late last night. poly and digit have finally found the crisp-collecting culprit — it turns out the jester's shoe size and hair color match the clues that were found! in gratitude, poly and digit agree to the servant with his current task of replacing all of the tables and chairs in the castle. his goal is to determine which furniture company should produce the new furniture. he receives information from a company that customizes elegant furniture, and he wants to analyze the company's production process in order to calculate some problems about cost and availability. read the following scenario, and assist poly and digit as they the servant with his calculations. the fit for a king furniture company requires 2020 hours of labor to produce a standard table, and a chair requires 1212 hours of labor. the labor available is 565565 hours per week. the company can produce at most 3535 chairs per week.

Anew 2-lane road is needed in a part of town that is growing. at some point the road will need 4 lanes to handle the anticipated traffic. if the city's optimistic estimate of growth is used, the expansion will be needed in 4 years and has a probability of happening of 40%. for the most likely and pessimistic estimates, the expansion will be needed in 8 and 15 years respectively. the probability of the pessimistic estimate happening is 20%. the expansion will cost $ 4.2 million and the interest rate is 8%. what is the expected pw the expansion will cost?