4) The data below shows N = f(t), the number of Facebook subscribers, in millions, worldwide at 3-month interval for one calendar year. Month, t Mar. Sep. 2011 Jun. Dec. Mar. 2011 2011 2011 2012 664.0 710.7 756.9 799.1 835.5 a) Calculate the average rate of change of N per month for the time intervals shown. Are these the values f'(t)? If not, how close are they? b) What can you say about the sign of d2n/dt2 for the 12-month period between March, 2011 and March, 2012? (Hint: Calculate a few values of the second derivative using your values from part a). Alternatively, a graph may make the answer obvious.)

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Exponential Growth Model

The relation that represents an exponential function is: