Ebola Outbreak in West Africa 5 3. Inection point and carrying capacity in the logistic growth model. (a) Use a plot of the data from Table 1 0r compute the average growth rate from month to month to determine the coordinates (t, N) for the inection point in the data. (b) Use implicit differentiation and substitution to determine the inection point of N ( c ) Combine the previous two parts to give an estimate for the carrying capacity, M. 4. Expression for N (t). (a) Solve the separable differential equation (1). (b) Use your growth rate from the exponential model for k and the carrying capacity from above for M to write N (t) representing the total number of cases of Ebola in West Africa at time t months. Graph N (t) for t = o, 1, 2, . . . , 24. (0) Compare the graph of N (t) to your sketch (in the previous section on exponential growth) depicting the behavior of the epidemic that you expect. 5 . Model predictions and verication. (a) Use your equation for N (t) to estimate the total number of cases of Ebola for times t = 5, 7, and 10 months. (b) Compare the predicted values from the previous part to the data in Table 1 and to the results from the exponential model in Part I. (0) Remark 0n the performance of the logistic model when used to depict the Ebola outbreak during its rst ten months. State your expectations for the performance and accuracy of the model for the duration of the epidemic. (d) Compare the results of the logistic growth model to the data reported by the World Health Organization for 1 S t S 24 in Tables 1 and 2. Show comparisons using both a table and a graph