(13) The best pizza crust is made from a natural yeast culture a sourdough starter-instead of dry com- mercial yeast. A starter is made by mixing together flour and water and then waiting for the mixture to ferment. An active starter contains various species of live yeast cells and the bacteria lactobacilli. (a) [10 points] When you make dough for your pizza, the first thing to do is feed your starter, by stirring more flour and water into the starter. As the yeast feeds on the flour, it produces carbon-dioxide, causing the volume of the starter to increase. As the starter grows, the yeast cells grow according to the logistic equation: dP/dt = .462P(1 P 2.5), where the population is measured in billions and time is measured in hours. What is the max- imum number of yeast cells that will grow in your starter? (b) [10 points] Assuming your culture starts with 1 million yeast cells, solve the differential equa- tion above to find an equation that models the yeast population in your starter over time. (c) [10 points] You realize on Wednesday that you want to make some pizza right after the calculus exam. You take the starter out of the refrigerator, when it is at a temperature of 40 degrees, and set it out in your 75 degree room. When the starter reaches 65 degrees you will feed it more flour and water. After an hour your starter has reached 50 degrees. At what time will you be able to feed the starter?