A common inhabitant of human intestines is the bacterium Escherichia coir} named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell ofthis bacterium in a nutrient-broth medium divides into two cells every:r 20 minutes. The initial population of a culture is 50 cells. {a} Find the relative growth rate. it": 3111(2) 4 hr1 {b} Find an expression for the number of cells after t hours. {c} Find the number of cells after 4 hours. 204800 f cells {d} Find the rate of growth after 4 hours. {Round your answer to the nearest integer.) 421,?11 x cellsfh {e} when will the population reach a million cells? (Round your answer to two decimal places.) xh A bacteria culture initially:l contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 230. {a} Find an expression for the number of bacteria after t hours. so = mules)t I {b} Find the number of bacteria after4 hours. [Round your answer to the nearest whole number.) 9(4) = .1393 J bacteria {c} Find the rate of growth aFter4 hours. (Round your answer to the nearest whole number.} p'[4] = 2331] x bacteria per hour (d) when will the population reach 10,000? [Round your answer to one decimal place.) .=_, .. The half-life of cesium-13? is 30 years. Suppose we have a ?D-mg sample. {a} Find the mass that remains aFter fyears. Fit} = {b} How much of the sample remains after 140 years? [Round your answer to two decimal places} x mg {c} After how long will only 1 mg remain? [Round your answer to one decimal place.) t: 133.9 .9 yr This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. The half-life of cesium-137 is 30 years. Suppose we have a 10 mg sample. Exercise (a) Find the mass that remains after t years. Step 1 Let y(t) be the mass (in mg) remaining after t years. Then we know the following. y(t) = y(0jekt = 10 10 . ekt Step 2 Since the half-life is 30 years, then y(30) = mg. Submit |Skip (you cannot come back) Exercise (b) How much of the sample remains after 40 years? Click here to begin! Exercise (c) After how long will only 1 mg remain? Step 1 To find the time at which only 1 mg remains, we must solve 1 = y(t) = 10(2 5/30), and so we get the following. t = -30 log2(A sample of a radioactive substance decayed to 94% of its original amount after a 1,fear. [Round your answers to two decimal places} {a} What is the half-life of the substance? :lvr {b} How long would it take the sample to decay to 65% of its original amount? :1\" {a} IfA is the area ofa circle with radius rand the circle expands as time passes, find o'Afo't in terms of drfdt. E :21: i d: -x m {h} Suppose oil spills From a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant late of 1 mfs, how fast is the area of the spill increasing when the radius is 32 m? 54:": f mzfs If a snowball melts so that its surface area decreases at a rate of 5 cm-/min, find the rate at which the diameter decreases when the diameter is 9 cm. 1 181 * cm/min