Problem 22 Hard Difficulty

After a 5.5-mg injection of dye, the readings of dye concentration, in mg/L, at two-second intervals are as shown in the table. Use Simpson's Rule to estimate the cardiac output.

Answer

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Video Transcript

Hello, My name is your GP Schmoke. And today we're going to be going over a question and Chapter eight section for the question says after a 5.5 milligram injection of dye, the readings of dye concentration and milligrams per leader at a two second interval are shown in the table. You Simpson's rule toe estimate the cardiac output. Now Simpson's rule says the integral from A to B ah function see of T is equal to Delta t over three times the quantity of sea of zero plus four times see of two plus two times CEO four plus four times see of six plus two times see of eight plus four time see of 10 plus two times see of 12 plus four times, CIA 14 and finally plus C of 16. Now, to translate this into the formula that we would use for our specific problem, it would be to over three times the quantity of zero plus four times 4.1 plus two times 8.9 plus four times 8.5 plus two times 6.7 plus four times 4.3 plus two times 2.5 plus four times 1.2 plus point to this would equal to 72 SRV 72 point five three. Now, to find the cardiac output, we would want to follow this formula F is equal to a which is the initial injection all over the integral from 0 to 16 which is shown in our table of sea of tea, which we calculated before as 72.53 This would be equal to 5.5 over 72 0.5 three. After you compute that, you would get the answer as 0.0 75 a or 0.76 around it which is milligrams per second or my bed. It would be leaders her second. And if you multiply this by 60 you would get four point five four nine or 4.55 if you rounded leaders per minute. Thank you