1. A physician finds that the cholesterol level of a patient on a diet can be ap
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Question
1. A physician finds that the cholesterol level of a patient on a diet can be approximated by C(t) 200+40e-0.1 where, t is the time (in months) since the patient began the diet. Find the average cholesterol level for the patient over the first six (6) months 2. The flow of blood is laminar (i.e., in layers), with the velocity very low near the arterial walls and highest in the center of the artery. A model of blood flow in the arteries assumes that the flow is made up of many layers of concentric tubes sliding one onto the other. Suppose R is the radius of an artery and r is the distance from a given layer to the center. The velocity of blood in a given layer is equal to where k is a numerical constant. Since the area of a circle is A-tr2, the change in the cross-sectional area of one of the layers, corresponding to a small change in the radius, dr, can be approximated by dA-2rrdr. The total blood flow in the layer is defined to be the product of velocity and cross-sectional area, or Set up and evaluate a definite integral to find the total arterial blood flow in the artery 3. If we assume that the average length (in cm) of an egg of width wcm is given by l-1.585w-0.487 Assume that an egg is approximately an ellipsoid. Find the volume of an ellipsoid centered at (0,.0), bounded in the upper halfplane by y - ba-^ad x--a on the left and x- a on the right by revolving this area about thex - axis using the dislk method. Using these results, show that the average volume V of an egg of width Wcm is given by z1.585w3-0.487wExplanation / Answer
1) Given that the approximate value of cholesterol can be calculated by the following formula:
C(t) = 200 + 40e-0.1t
where, t= number of months since the patient begins the diet.
Therefore, if t = 6 months, then substituting the value of 't' in the above equation we will have,
C (6) = 200 + 40e(-0.1 x 6) = 221.95
Therefore, the approximate amount of cholesterol in the patient since he started the diet six months ago will be 221.95.
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