1. Consider a petri dish that initially contains 100 bacteria. Let B(t) be the total population size at time t in hours. Each bacterium produces a new bacterium at rate 0.5 per hour. Thus in total the rate of increase in the population size due to births is 0.5B bacteria per hour. Bacteria are lost from the petri dish due to death; in total the rate of decrease in the population size due to deaths is 0.125 B' bacteria per hour. Write a differential equation describing the overall rate of change of B. Solve the equation to isolate an expression for B(t) at any time. (Hint: the algebra may be simpler if you replace 0.5 with 1/2 and 0.125 with 1/8.)