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- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?Radioactive Decay The amount of radioactive isotope thorium-234 present in a certain sample at timet is given by A(t) = 500e-0.02828tgrams, where tyears is the time since the initial amount was measured. How long will it take for the amount of isotopeto equal 318 grams?Uranium 239 is an unstable isotope of uranium that decays rapidly. In order to determine the rate of decay, 1 gram of U239 was placed in a container, and the amount remaining was measured at 1-minute intervals and recorded in the table below. (Let t be the time in minutes and U the number of grams remaining.) Timein minutes Gramsremaining 0 1 1 0.9710 2 0.9428 3 0.9155 4 0.8889 5 0.8632 (a) Show that these are exponential data. (Round your answer to three decimal places.) The ratios of successive terms are always , and therefore the data are exponential. (b) What is the percentage decay rate each minute? (Round your answer to one decimal place.) %What does this number mean in practical terms? This means that % of the remaining uranium decays each minute. (c) Use functional notation to express the amount remaining after 7 minutes. U( ) Calculate that value. (Round your answer to three decimal places.) g(d) What is the half-life of U239? (Round your answer to…
- The rate of disintegration of a radioactive substance is proportional to the amount of the substance present at any instant. In 1962, an experiment on Strontium-90 (Sr90), a radioactive substance usually found in nuclear fall out, was started. A certain amount (in grams) of Sr90 was initially placed in a sealed container. In 1987, it was found that the Sr90 had reached its half-life. Further, it was observed that 7.5 grams remained in the container in 1970. How much Sr90 was initially stored for the experiment? How many years after half-life will it take to reduce the substance to just 12% of its initial valueOil leaked from a tank at a rate of r(t) per hour. The rate decreased as time passed and values of the rate of two-hour time intervals are shoen in the table. Find lower and upper estimates for the total amount of oil that leaked out .A tank contains 2220 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 6 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. Find the amount of sugar after t minutes. y(t)=
- For some measuring processes, the uncertainty is approximately proportional to the value of the measurement. For example, a certain scale is said to have an uncertainty of ±2%. An object is weighed on this scale. a) Given that the reading is 100 g, express the uncertainty in this measurement in grams. b) Given that the reading is 50 g, express the uncertainty in this measurement in grams.The number N of trees of a given species per acre is approximated by the model N = 2000(10−0.12x), 3 ≤ x ≤ 30 where x is the average diameter of the trees (in inches) 4.5 feet above the ground. Use the model to approximate the average diameter (in inches) of the trees in a test plot when N = 27. (Round your answer to two decimal places.)Oil leaked from a tank at a rate of r (t) liters per hour. Therate decreased as time passed and values of the rate at twohourtime intervals are shown in the table. Find lower andupper estimates for the total amount of oil that leaked out.
- a police personnel discovers the body of a dead person presumably murdered. the body is located in a room that is kept constant at 70F at10:40pm, the body temperature of the victimme was measured at 94.4F. ANother measurement of the body was taken after 90 mins, and was 89F. Estimate the time of death assuming that the victimrs temperature was normal at 98.6F at the time of deathThe rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(t) = −0.18t2 + 3t + 15 gallons per year (0 ≤ t ≤ 10), where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction f(t) =√0.2 + 0.04t of all bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2008 to the start of 2010. HINT [Rate of consumption = s(t)f(t).] ____________ galThe rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(t) = −0.18t2 + 3t + 15 gallons per year (0 ≤ t ≤ 10), where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction f(t) = 0.2 + 0.04t of all bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2004 to the start of 2010. HINT [Rate of consumption = s(t)f(t).]