A culture of bacteria in a particular dish has an initial population of 200 cells grows at a rate of N'(t) = 40e-2/465t cells/day. a. Find the population N(t) at any time t = 0. b. What is the population after 9 days? a. Find a formula for the number of cells, N(t), after t days. N(t) = (Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)Starting with an initial value of P(0) = 20, the population of a prairie dog community grows at a rate of P'(t) = 20- , (in units of prairie dogs/month), for Ost = 40. a. What is the population 14 months later? b. Find the population P(t) for Ost = 40. a. After 14 months, the population is prairie dogs. (Type a whole number. Round to the nearest prairie dog as needed.)An oil refinery produces oil at a variable rate given by the following equation, where t is measured in days and Q is measure in barrels. 700 if Ost