The numbers of U.S. bank failures are shown in Table 74 for various years.

Let y be the number of bank failures in the year that is x years since 2010.
a. Construct a scatterplot.
b. Use two points to find an equation of an exponential model.
c. Graph the model on the scatterplot. Verify that the model passes through the two points you chose in finding the equation in part (b) and that it comes close to all of the data points.
d. What is the coefficient a of your model = abx? What does it mean in this situation?
e. Use the model to estimate the number of banks that failed in 2014. Compute and interpret the residual.

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Table 74 Numbers of U.S. Bank Failures Year Number of Bank Failures 2010 2011 2012 2013 2014 157 92 51 24 18