12. The number, N, of bacteria in a culture at time t, irt hours, is Mr) = 1000[30 + {in a. What is the initial number of bacteria in the culture? b. Determine the rate of change in the number of bacteria at time 1. c. How fast is the number of bacteria changing when r = 20'? d . Determine the largest number of bacteria in the culture during the interval [l E r E 50. e. What is happening to the number of bacteria in the culture as time passes