Show transcribed image text written in fraction notation, mixed number notation, or decimal HatiuulI, that you think is most appropriate for the problem. Do Not Round unless specified by the problem. All fractions must be written in lowest terms. All answers must be written in the appropriate simplified form. 1) A bacteria colony which is unrestricted in its growth will grow out in a circular manner. The population P(t) of the colony at time t is directly proportional to the area of the circle. Suppose that a particular bacteria grows in such a way that the population doubles every day, and that initially (t=0) the colony has a radius of 2 centimeter and a population of 5 million. a) Find the Population and Radius of the colony on the fifth day. P(5) = 2 b) Find the Rate of Change of the population and radius of the colony on the fifth day r'(5) = c) Unrestricted growth models are often impractical as values will quickly become unreasonable. On what day does our model predict that the area of the bacteria colony will be 1 square mile? Time (in Days) 2) Consider the function f (x) = x(x *). Use Logarithmic Differentiation to find f (x). f (x)