68. Metabolic Rate The basal metabolic rate (in kcal/day) for large anteaters is given by y = f(x) = 19.7x0.753 where x is the anteater's weight in kilograms.* Source: Wild- life Feeding and Nutrition. a. Find the basal metabolic rate for anteaters with the follow- ing weights. i. 5 kg ii. 25 kg b. Suppose the anteater's weight is given in pounds rather than kilograms. Given that 1 1b = 0.454 kg, find a func- tion x = g(z) giving the anteater's weight in kilograms if z is the animal's weight in pounds. c. Write the basal metabolic rate as a function of the weight in pounds in the form y = az by calculating f(g(=)).49. Length of Life According to recent data from the Teachers Insurance and Annuity Association (TIAA), the survival func- tion for life after 65 is approximately given by S(x) = 1 - 0.058x - 0.076x2, where x is measured in decades. This function gives the prob- ability that an individual who reaches the age of 65 will live at least x decades (10x years) longer. Source: Ralph DeMarr. a. Find the median length of life for people who reach 65, that is, the age for which the survival rate is 0.50. b. Find the age beyond which virtually nobody lives. (There are, of course, exceptions.)33. Growth of Bacteria Salmonella bacteria, found on almost all chicken and eggs. grow rapidly in a nice warm place. If just a fellar hundred bacteria are left on the cutting board when a chicken is cut up. and they get into the potato salad, the popula- tion begins compotmcliug. Suppose the number present in the potato salad after t hours is given by Hi) = 500 ' 23'. a. If the potato salad is left out on the table, how many bacte- ria are present 1 hour later? h. HoeF many were present initially? c. How often do the bacteria double? cl. How quickly 1will [be number of bacteria increase to 32.000\"? 78. Bald Eagle Population The U.S. Fish & Wildlife Service has monitored the number of bald eagle breeding pairs in the lower 48 states. In Exercise 41b of the previous section, the number of pairs was modeled by the exponential function f(t) = 487(1.0723 ), where t = 0 corresponded to 1963. Source: U.S. Fish & Wild- life Service. If this trend continues, when will the number of bald eagle breeding pairs be double the 2006 level of 9789?14. Iiiecayr of liladinactivityr A large cloud of radioactive debris from a nuclear explosion has oated over the Pacific North- west, contaminating much of the hayr supply. Consequently, farmers in the area are concerned that the cows who eat this hay will give contaminated milk. {The tolerance level for ra- dioactive iodine in milk is ill.) The percent of the initial amount of radioactive iodine still present in the ha};r after 1* days is ap- prosimated by P\"), which is given by the mathematical model Flt] = lune\"1'. a. Find the percent remaining after 4 days. I}. Find the percent remaining after 10 days. c. Some scientists feel that the hay is safe after the percent of radioactive iodine has declined to 10% of the original amount. Salve the equation 10 = Imus-" to nd the nullit- her of days before the hay may he used. d. Other scientists believe that the hay is not safe until the level of radioactive iodine has declined to only 1% of the original level. Find the number of days that this would take