Tim has 3 dice, one with 4 sides, 5 sides, and 6 sides. Each dice is fair and has faces (1, 2, ... n) where n is the number of sides. Tim proceeds as follows: he rolls each die one at a time (starting with the four-sided, then five, then six). However, if Tim ever rolls more than a three he stops rolling the dice. Let X be the sum of all the dice Tim rolled.1. Compute E[X].2. Compute P(A). Where A represents the event that Tim rolled a five with one of the die.

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?