Joe knows from experience that on average it takes thirty-five minutes to mow his yard. He really needs to mow the yard, but the big game kicks-off in forty-five minutes and he really wants to see that too. His DVR is not working and he really needs to mow that yard. If he starts right now, what is the probability that he can finish mowing the yard before the start of the game? Draw the graph that would illustrate this problem and compute the probability assuming that yard mowing follows an exponential distribution.

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?