Taylor Problem 11.10, modified: You know that the average rate of decays from a particular radioactive sample is roughly 20 per minute. (Assume that the radioactive half-life is extremely long, so that the decay rate is essentially constant over time.) Suppose that you want to measure this rate more precisely. a. (2 pts.) If you were to make a single measurement of counts from this sample for one minute, what is the approximate percentage uncertainty in your measurement? Show your work. b. (2 pts.) If you wanted to measure the decay rate to within an uncertainty (standard deviation) of 5% using a single long integration, approximately how many minutes should you integrate counts from this sample? Show your work. c. (1 pt.) If you wanted to measure the decay rate to within an uncertainty of 1% using a single long integration, approximately how many minutes should you integrate counts from this sample? Show your work. d. (1 pt.) In general, if you double the length of time that you integrate the counts from any sample, by what factor does your uncertainty decrease