2. Now imagine dividing the administered drug into N pieces instead of 10. (For instance, if you were calculating things ten minutes at a time, N would be 60.) Using E notation, write down expressions for an upper bound on the remaining amount of antibiotic, a lower bound, and the average. 3. Now take the limit as N - co. Write down a definite integral that gives the exact amount of remaining drug. You are not expected to evaluate this integral.Drug Titers: When you take an antibiotic, the concentration of the drug in your body (the drug titer} rst shoots up but then decays exponentially. If you take in a quantityr A of the drug, there there will be Ae'\" left after a time t, where r is the rate at which your body breaks down or otherwise elhninates the antibiotic. {The same idea applies to alcohol and other poisons in your system. but we'll stick. to antibiotirn.) Here we consider the drug titer of an antibiotic that you take mntrnuously. as with an IV drip. Q Suppose that you reeeive mining of an antibiotic coatmnouslv over a period of 10 hours. We will compute the amount of antibiotic in your body at the end of that period1 assuming that your body eliminates the antibiotic at a rate of 4% per hour. For this problem, it is convenient to let i represent how long ago you received the dmg. That is, t = l] is the current time1 t = l is one hour 330: i: 2 is two hours ago, and the mediostion started at t = 10. That way, WE only 115W? to consider positive values of t and the e'eet of the medicine administered at time t gets downgrade! by a factor of e'\". a.) Consider the portion of the drug that was administered in the past hour. that is between t = [l and t = 1. Find upper and inner bounds for how much of that drug remains in your both.r at time t]. b) Repeat for the portions administered between t = I andt = 2, between t = 2 and t = 3. and so on up to the portion administered between i=9nndi=l. e) Add up the pieces to get upper and lower bounds for the remaining amount of the entire IV drip. d} Average these upper and lower bounds to get a good estimate for how much drug is currentlyr in your body