Maths coursework Essay Example | Topics and Well Written Essays - 1000 words

Maths coursework - Essay Example Although the function "y=10e^ (-0.175t)", slightly differ from the given values of the graph (between hour 4-7). However, for the all other points, the graph follows the same path as the one given. So we can say that the function "y=10e^ (-0.175t)", is suitable to model the data of the graph. Figure 3 represents the amount of the drug in the bloodstream over a 24-hour period. In the below graph (figure 3) assumption is made that after every six hour 10 Â µg of drug is given to patient and it adds in the drug remained in the bloodstream ( value of constant a in function "y=10e^ (-0.175t)", will change after every six hours). Therefore, the function will change after every six hours as the remaining drug adds into the given drug every six hours. Initially the drug given was 10 Â µg. After six hour, it remains to 3.5 Â µg. Now when 10 Â µg is again give to patient then it will become 13.5 Â µg. Moreover, this pattern will be continues for every six hours. Since we wanted to plot for 24-hour period, so for the second, third and fourth period the function will be " y=13.5e^ (-0.175(t-6)) ", " y=14.7e^ (-0.175(t-12)) "and" y=15.1e^ (-0.175(t-18)) " respectively. The value of t is changed here, so that the graph plotted continuous from the last point, other wise it will start from the starting point. From the figure 5, it can be seen that, when after initially 10Â µg of drug is given to the patient and thereafter no drug is given to the patients then the function "y=10e^ (-0.175t)" is when plotted for week period, the value of y approaches to 0 (actual value will be 0.0524 Â µg) after 30 hours. However, it will never become zero. Figure 6 represents the amount of the drug in the bloodstream over a 24-hour period. In the above graph assumption is made that after every six hour 10 Â µg of drug is given to patient and it adds in the drug remained in the bloodstream ( value of constant a in function "y=10e^ (-0.175t)", will change after