3 2 5 log log log 25 x 41 The number of students in a school infected with the

3 2 5 log log log 25 x 41 the number of students in a

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3 2 5 log (log (log 25)) x 41. The number of students in a school infected with the flu t days after exposure is modeled by the function   4 300 1 t P t e . (a) How many students were infected after three days? (b) When will 100 students be infected?
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Solve. Show all steps. Give decimal answers correct to three decimal places. 42. Exponential growth is modeled by the function 0 kt n n e . A culture contains 500 bacteria when t = 0. After an hour, the number of bacteria is 1200. (a) How many bacteria are there after four hours? (b) After how many hours will there be 8000 bacteria? __________________________________________________________________________________________ Evaluate. 43. 1 3 tan Cos 2 44. sec Arcsin 2 2 45. 1 cos Sin 2 x 46. sec Arctan 4 x __________________________________________________________________________________________ 47. Convert the equation 2 3 8 x y into polar form. 48. Convert the equation 2 2 sin 0 r r into rectangular form. __________________________________________________________________________________________ Make a table, and sketch the graph. 49. 3sin r 50. 2 2cos r 51. 1 2sin r 52. 3 2cos r 53. 4cos 3 r 54. 3sin 2 r __________________________________________________________________________________________ Write a function for each problem, and use your graphing calculator to solve. Give decimal answers correct to three decimal places. Be sure to sketch the graph you used, and label it with your answer. 55. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals, as shown. What dimensions should be used so that the enclosed area will be a maximum? 56. A rectangle is bounded by the x -axis and the semicircle 2 25 y x as shown. What length and width should the rectangle have so that its area is a maximum? 57. Four feet of wire is to be used to form a square and a circle. Find the length of the sides of the square and the radius of the circle that will enclose the maximum total area?
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