MA 241 3.3:

1)

A car's cooling system has a capacity of 20 quarts. Initially, the system contains a mixture of 4 quarts of antifreeze and 16 quarts of water. Water runs into the system at the rate of 1 , mi then the homogeneous mixture runs out at the same rate. In quarts, how much antifreeze is in the system at the end of 5 minutes? (Round your answer to two decimal places.) qt800 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The volume of the lake including the pesticide is 10" gallons. A river flows into the lake bringing 5,000 gallons of fresh water per minute, and the uniform mixture spills over the dam at the same rate. How long, in minutes, will it take to reduce the pesticide in the lake to a safe level of 1 part per million gallons? (Round your answer to the nearest minute.) minA tank contains 500 gallons Di salt-free water. A brine containing 0.25 lb of salt per gallon runs into the tank at the rate of 1 , and the well-stirred mixture runs nut at 1 . In pounds per gallon, what is the concentration of salt in the tank at the End of to minutes? {Round your answerto four decimal places) lbs per gal Radium decays exponentially; it has a half-life of 1,600 years. Find a formula for the amount, q((), remaining from 70 mg of pure radium after f years. q(t) After how many years will there be 10 mg left? (Round your answer to the nearest year.) yrA 3-D printer was purchased for $20,000 and had a value of $12,000 after 2 years of use. Assuming that the value is decreasing exponentially, find the value of the printer after 8 years of use. (Round your answer to the nearest dollar.) $Suppose that $10,000 is invested in an account for which interest is compounding continuously at 3.14%. What is the value after 5 years? After 10 years? (Round your answers to two decimal places.) 5 years $ 10 years $ After how many years will the original investment be doubled? (Round your answer to two decimal places.) yrThe Lincoln wheat penny was designed by Victor D. Brenner in 1909. Currently, the most valued penny is the 1909 5 VDB penny. It was minted in San F and only 484,000 were minted with the initials on the back. k. In 2015, the S VDB penny in uncirculated condition is worth $3,200. When will it be worth $15,000? (Round your answer to the nearest year.)The temperature in a hot tub is 1040 and the room temperature is 75. The water cools to 90 in 10 minutes. What is the water temperature after 20 minutes? (Round your answer to one decimal place.) After how many minutes will the temperature be 80*? (Round your answer to one decimal place.) minThe population of the United States has grown at different rates over ten-year increments as shown by the following table. Year Population of U.S. 1930 123.1 million 1940 132.1 million 1950 152.3 million 1960 180.7 million If the maximum supportable population of the U.S. is 600 million people, use the logistic model to predict the population (in millions of people) of the U.S. in 2010 by using the following years as data points. (Round your answers to one decimal place.) (a) using 1930 and 1940 as data points million people (b) using 1950 and 1960 as data points million people Compare/contrast/explain the different results. The growth rate from part (a) is [ ---Select--- : the growth rate from part (b).