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#23 and 29, differentiate the function
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- 11.Suppose that during a controlled experiment, the temperature in a test tube attime t is rising at a rate of 6t^2+2 degrees centigrade per minute. If the initialtemperature is 20°C, what is the temperature in the test tube after 10 minutes?The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.97x2.1 for one year to y = 0.35x2 + 0.65x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) before after
- The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1) where x=0 corresponds to year 1990. A) How many pounds of Aluminum were shipped in 2004 B) Assuming the continued accuracy of the model when will aluminum shipments reach 247,400,000,000 pounds.
- A group of survivors on a supply run has returned to their base camp with a population of 2000. Two of them were bitten by zombies but didn’t tell anyone. If it is assumed that the rate at which the virus spreads is proportional not only to the number x of infected people but also to the number of people not infected, determine the number of infected residents after 14 days if it is further observed that after 6 days, 50 residents got infected. What is the time at which half of the population will become infected if nothing is done? How many people will be NOT be infected after 2 weeks if nothing is done? A rescue helicopter saved 40 survivors. How long did they have to survive?For the production function Q (K,L)= 1000 (KL3 )1/3 , Given the current input level K = 400 and L = 40. Use marginal analysis to estimate the approximate change in output which results form an increase in K of 9 units and a decrease in L of 7 units. Verify that Young′s Theorem holds?Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec from the tank and, at the same moment, a valve is opened that lets in a 1% solution (a 1% concentration) of chlorine at a slower rate of 2 gal/sec. A.) When is the tank half full and what is the concentration of the chlorine then? B.) If the drain is closed when the tank is half full and the tank is allowed to fill, what will be the final concentration of chlorine in the tank?
- It is estimated that t years from now the population of a certain lakeside communitywill be changing at the rate of 0.6t2 + 0.2t + 0.5 thousand people per year.Environmentalists have found that the level of pollution in the lake increases at the rateof approximately 5 units per 1000 people. By how much will the pollution in the lakeincrease during the next 2 years?The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.