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 of this bacterium in a nutrient-broth medium divides into two cells ever\").r 2-1] minutes. The initial population ofa culture is 50 cells. {a} Find the relative growth rate. {b} Find an expression for the number of cells after t hours. {c} Find the number of cells after 4 hours. 204800 ( 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.) w A bacteria culture initially,r contains 10!] cells and grows at a rate proportional to its size. After an hour the population has increased to 230. (c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.) P'(4) = 2330 * bacteria per hourThe half-life of cesium-13? is 30 years. Suppose we have a ?D-mg sample. {a} Find the mass that remains aer t years. Hf} = (b) How much of the sample remains after 140 years? (Round your answer to two decimal places} x mg 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 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(2-1/30), and so we get the following. t = -30 log2A sample of a radioactive substance decayed to 94% of its original amount after a 1Jurear. [Round your answers to two decimal places} {a} what is the halflife of the substance? :1\" {b} How long would it take the sample to decay to 65% of its on'ginal amount? :1\