Applications of Derivative (Exponential Growth and Decay)

Exercise 6 2. The number of bacteria present in a culture after t hours can be approximated by N = 2000e0 (a) According to this model, what is the initial number of bacteria in the culture? (b) Use the model to estimate the average rate of increase in the number of bacteria in the culture over the first 5 hours. (c) Use the model to estimate the instantaneous rate of growth in the number of bacteria after 5 hours. A culture has 5000 bacteria after 15 minutes and 40 000 bacteria after one hour. The number of bacteria present after t hours can be modeled by N = Noekt , where No is the initial number of bacteria present. (a) (b) (c) (d) Find the values of No and k. When will the number of bacteria be 150 000? Find the average rate of growth in the number of bacteria over the first 15 minutes. Find the instantaneous rate of growth in the number of bacteria after 15 minutes. 27