1. At time t = 0 minutes, the temperature of a cup of coffee is 180 degrees Fahrenheit. Left in a room
whose temperature is 70 degrees Fahrenheit, the coffee cools so that its temperature function T(t),
also measured in degrees Fahrenheit, satisfies the differential equation * = - T +35.
(a) Find an expression for T(t) using the initial condition T(0) = 180.
(b) Find lim T(t). Explain what this limit means in the context of the problem.
(c) At what time t is the temperature of the coffee decreasing at the rate of 15 degrees Fahrenheit per
minute? How hot is the coffee at that point? Indicate units of measurement.

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.