For number one, you need to find A. For extended delay type, input t as 24 then equal it to 0 (in this case, 10 is the limit for the extended type. Look at the graph) Then isolate A by dividing the function, so it should be 10/ (surge function). You can't do the same with medium and rapid since their limits are 100 and requires different time t value You need to take derivative to get t and then like before input the t value to the specific function and equal it to 100 to get A Number 2, I'm not too sure, but you need to compute integrals to get the area under the curve. The area is the maximum treatment effect. For Number 3a do another integral from O to 24 for the chosen delay type. For 3b compute an integral from. 24 to infinity. You're allowed to use a calculator for number 1 and 2 only via instructions provided I believe you must show your work for number 3 so I hope you are good doing improper integrals and integration by parts. A surge function is a function of the formf(t) = At" e( bt)The values A, n, and b are the parameters of the function.This function accurately represents the way a drug interacts in the bloodstream. Studyingthis function is essential to doctors and pharmacists because it allows them to administerdosages of medicine correctlyA drug dose is being designed for a 100kg female patient. The amount of the drug in thepatient's bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is givenby a surge function.Any positive value of A can be achieved by increasing or decreasing the amount ofmedicine given. However, depending on the type of delayed release mechanism selectedthere are choices possible for the value of the pair (n,b): The achievable pairs are listed inthe table below.Delay Type n value b valueExtended 20.2Medium30.4Rapid30.6The medical requirements for the treatment are:• The dose (in ng/ml) may not exceed 100 at any time.The dose must fall to be at or below 10 ng/ml by 24 hours.Within these parameters, the treatment effect will be measured in ng/ml-hours. (1ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtainthe maximum possible treatment effect while ensuring the requirements are met. Project instructions1. For each Delay Type, determine the value of A (dosage amount) that maximizes treat-ment effect for that Delay Type while meeting medical requirements.2. Determine which Delay Type (assuming optimal dosage) will maximize treatment ef-fect.3. For the Delay Type and dosage level you selected,(a) determine the exact treatment effect over the first 24 hours.(b) determine the residual treatment effect for time after the first 24 hours.Note: For parts (1) and (2) you may use numerical tools (computer/calculator/etc) aslong as you reach a decimal accuracy of two decimal places, and clearly describe exactly howyou use those tools to obtain your result. You may also find a graphing tool to be usefuloverall for visualizing the problem. A graph for the "Rapid" delay pattern is available here:https://www.desmos.com/calculator/epsu7qu2t9

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Answered: A surge function is a function of the…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ