Problem 1. During the pandemic a baker discovered that she was unable to obtain yeast (due to the huge number of self-isolated people deciding to bake.) So she decided to make up a batch of sour-dough. This entails starting a natural wild yeast culture and feeding" it with flour and water once a day. Her bread baking book says that to feed the culture she must throw out 80% of her culture and replace it with flour and water. Let's suppose that the yeast population follows a logistic model: y' = ay(1 y) where y represents the proportion of yeast that can subsist on the available flour. She concludes that if the yeast starts with 20% of the maximum then it takes it one day to eat up most of the flour. Assume that starting with a 20% yeast solution it takes it a day to expand to 90% of capacity. i.) Plot the phase diagram of possible solutions and discuss the stability of each fixed solution. Indicate which region best models this experiment. ii.) Solve the equation given the initial value y(0) = 0.2. iii.) Calculate a based on the conditions stated in the problem. iv.) If the baker forgot to "feed her culture after one day, how much has the yeast filled its capacity after two days. Problem 1. During the pandemic a baker discovered that she was unable to obtain yeast (due to the huge number of self-isolated people deciding to bake.) So she decided to make up a batch of sour-dough. This entails starting a natural wild yeast culture and feeding" it with flour and water once a day. Her bread baking book says that to feed the culture she must throw out 80% of her culture and replace it with flour and water. Let's suppose that the yeast population follows a logistic model: y' = ay(1 y) where y represents the proportion of yeast that can subsist on the available flour. She concludes that if the yeast starts with 20% of the maximum then it takes it one day to eat up most of the flour. Assume that starting with a 20% yeast solution it takes it a day to expand to 90% of capacity. i.) Plot the phase diagram of possible solutions and discuss the stability of each fixed solution. Indicate which region best models this experiment. ii.) Solve the equation given the initial value y(0) = 0.2. iii.) Calculate a based on the conditions stated in the problem. iv.) If the baker forgot to "feed her culture after one day, how much has the yeast filled its capacity after two days