Suppose that we would like to estimate the total number of counties in the us. the uscounties data file contains information on the number of counties in each state, as well as the land area and population (the data file isn't necessary to answer this question.)

sample 1 contains a sample of 30 states randomly selected with probability proportional to the land area of each state (with replacement); sample 2 contains a sample of 30 states randomly selected with probability proportional to the population of each state (with replacement).

(a) which of the above samples (land area or population count) would you expect to provide a better estimate of the total number of counties in the us?

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?