Peanut allergies are becoming increasingly common in Western countries. Some evidence points to the timing of peanuts' first introduction in the diet as an influential factor, raising the question of whether pediatricians should recommend early exposure or avoidance. A study enrolled infants with a diagnosed peanut allergy and randomly assigned them to either completely avoid peanuts or consume peanuts in small amounts regularly until they reached 6060 months of age. At the end of the study, 1818 of the 5151 infants who had avoided peanuts were still allergic to peanuts. In contrast, 55 of the 4747 infants who had consumed peanuts were still allergic to peanuts. Required:
a. What are the two variables described?
b. How many infants do these data represent?
c. How many of them were assigned to avoid peanuts during the study?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?