Question 1:

1. [13 pts] Two different bacteria colonies are growing near a pool of stagnant water. Suppose that the first colony initially has 1000 bacteria and doubles every 21 minutes. The second colony has 710,000 and doubles every 33 minutes. a. Find the growth equations for each colony as a function of elapsed time in minutes. b. How much time will elapse before the first colony becomes as large as the second? c. Compute the doubling time for both colonies. 2. [12 pts] A cosmetic company is planning the introduction and promotion of a new lipstick line. The marketing research department, after test marketing the new line in a carefully selected large city, found that the weekly revenue in that city is given approximately by ROI) = 10x3" 0 s x s 2, where 3: thousand lipsticks were sold per week. a. Find the average rate of change of the weekly revenue in the interval [0.5, 1.5]. Interpret your result.| b. Find R'(D.8) and interpret the result. c. Find R'(1.2) and compare your result with what you found in part {b}. What can be said about weekly revenue at these two xvalues