We are going to fence in a rectangular field. If we look at the field from above, the cost of the vertical sides are $10/m, the cost of the bottom is $2/m and the cost of the top is $7/m. If we have $700, determine the dimensions of the field that will maximize the enclosed area. Be sure to use the second derivative test, to verify whether the critical point(s) represent a maximum.

3} The number of bacteria in a culture, N, at time t is given by NO) = 200({30He 5] ' a. When is the rate of change of the number of bacteria equal to zero? b. If the bacteria colonyr is placed in a colonyF of mice, the number of mice that become infected, M, is related to the number of bacteria present by the equation M0) = {lN +1000. After 10 days, how many mice are affected? {Round the answer to the nearest whole number)