The initial population in a bacteria colony is 10,000. After t hours, the colony has grown to a number P(t) given by P(t) = 10,000(1+0.86t+t) A. Find the rate of change of the population P with respect to time. This is also known as growth rate. B. Find the number of bacteria present after 5 hours. C. Find the growth rate when t=5. 7. A company determines that the monthly sales S, in thousands of dollars, after t months of marketing a product is given by S(t) = 2t -40t +220t +160 (Hint: graph the function, viewing window: x min 0, max 22, scale 2; y min150, max 600, scale 25) A. Find the monthly sales after 1 month; 4 months; 6 months; 9 months and 20 months B. Find the rate of change S'(t). C. Find the rate of change at t = 1; t = 4; t = 6;t=9;t=20