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Unformatted text preview: Get stepbystep solutions for your textbook problems from www.math4u.us 1. A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function ( ) p kt S t At e = is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.01, p = 4, k = 0.07, and is measured in minutes, estimate the times corresponding to the inflection points and explain their significance. If you have a graphing device, use it to graph the drug response curve. 2. If the initial amount A o of money is invested at an interest rate r compounded n times a years is 1 nt o r A A n = + If we let n → ∞ , we refer to the continuous compounding of interest. Use l’Hopital’s Rule to show that if interest is compounded continuously, then the amount after t years rt o A A e = . 3. A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence? 4. A box with a square base and open top must have a volume of 32,000 cm 3 . Find the dimensions of the box that minimize the amount of material used. 5. If 1200 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box. 6. A rectangular storage container with an open top is to have a volume of 10 m . The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. 7. Find, correct to two decimal places, the coordinates of the point on the curve y=tan x that is closest to the point (1,1). 8. Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. 9. Find the area of the largest rectangle that can be inscribed in the ellipse x 2 /a 2 + y 2 /b 2 = 1. 10. Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle. 11. Find the dimensions of the rectangle of largest area that has its base on the xaxis and its other two vertices above the xaxis and lying on the parabola y=8  x 2 . 12. Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r. 13. Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the legs. 14. A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder. Get stepbystep solutions for your textbook problems from www.math4u.us 15. A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder.possible volume of such a cylinder....
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This note was uploaded on 07/18/2011 for the course ECON 1001 taught by Professor Microeconomics during the Spring '11 term at Hong Kong Shue Yan.
 Spring '11
 Microeconomics
 The Land

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