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having some issues on a review test and would like some help with 2,3,4,5,6 Note: For questions 2-4 we assume the discrete-time dynamical system is

having some issues on a review test and would like some help with 2,3,4,5,6 image text in transcribed

image text in transcribed Note: For questions 2-4 we assume the discrete-time dynamical system is given by mt+1=0.7mt+3withm0=0. Please note that this system is NOT the answer to question 1. 2. Write an excel document that calculates the medication levels in the bloodstream for the first four weeks of taking this medication (i.e., for 28 days). Include your excel table, or fill in the table that follows the cover page. From this calculation, we can see that in the long term the level of medication in the bloodstream is going towards what value? (Round the amount on the 28th day to the second decimal place.) The next two paragraphs walk you through how to use Excel (using a different example). Suppose your dynamical system were mt+1=0.2mt+4 with m0=10. To do the excel calculations, you would type the following into a spreadsheet, where A1 would have your initial amount, in this case it is 10 . A2 is calculating 20% of A1 or 0.2A1 and then 4 is added. A3 is calculating 20% of A2 or 0.2A2 and then 4 is added, and so on. The first spreadsheet shows what you would type in a cell (or box), and the second spreadsheet is what the computation would display. The second spreadsheet is what we are looking for you to submit. Note that once you set up the first formula (in the cell A2 in this case, you can copy/drag the formula down into the next rows.) 3. Find the equilibrium point(s) of this system. 4. Sketch a graph of the updating function of the discrete-time dynamical system mt+1=0.7mt+3. You can think of the updating function also as y=0.7x+3, but please label your graph using the notation mt and mt+1 in place of x and y. Draw a cobwebbing diagram that determines whether the equilibrium point(s) are stable or unstable. (You will want to choose initial conditions near the equilibrium point(s), on each side, to check for stability.) Does this answer agree with what you would have expected from Note: For questions 5-6, we change the daily dose. For a daily dose of dmg/liter the system is given by: mt+1=0.7mt+d,withm0=0. 5. What would the equilibrium concentration be in this case? Give your answer as an expression involving of d. 6. Suppose that a doctor wants to give the patient a daily dose such that eventually the concentration of medication will be 20mg/liter. What should that dose, d, be

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