A case of vintage wine appreciates in value each year, but there is also an annual storage charge. The value of a typical case of investment-grade wine after t years is  V(t) = 2000 + 40 sqrt(t)− 10t dollars (for 0 ≤ t ≤ 25).Find the storage time that will maximize the value of the wine.t =

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

Following surgery, a patient has been receiving a pain relief medication intravenously. The concentration C (in milligrams per liter) of the medication in the patient's bloodstream t hours after this process started is given by C(t) a) The patient will not receive pain relief unless the concentration of the medication is 20 or more milligrams per liter. Use this function to determine the time interval for which the concentration of the medication, C, will be greater than or equal to 20 milligrams per liter. 60t + 12 t + 6 ,t≥ 0 The time interval for which the patient will receive pain relief is hours. (Express your answer in interval notation and round any decimals to the nearest tenth of an hour). b) If the intravenous medication continues to be given to the patient (that is, as time goes on and t approaches ∞), the concentration will approach milligrams per liter.

In this model, the period immediately after the stock is issued offers excess returns on the stock—that is, the stock is selling for more than it is really worth. One such model for a class of Internet IPOs predicts the percent overvaluation of a stock as a function of time as R(t)=250(t2/(2.718)3t) where R (t) is the overvaluation in percent and t is the time in months after the initial issue. a. Use the information provided by the first derivative, second derivative, and asymptotes to prepare advice for clients as to when they should expect a signal to prepare to buy or sell (inflection point), the exact time when they should buy or sell (local maximum and minimum), and any false signals prior to a horizontal asymptote. Explain your reasoning. please type answer.