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Get step-by-step 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 x-axis and its other two vertices above the x-axis 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.
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Get step-by-step 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.
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