Question: The number of US business bankruptcies for various years are listed below.

(Source: Administration Office of the U.S. Courts)

1. What about this data suggests that a quadratic model is likely to be the more
   appropriate than a linear or exponential model?
2. Use regression to find a reasonable quadratic model, \(f\left( t \right)\), that represents the bankruptcies (in thousands) for the year that is t years since 1990. (Round values to three decimal places.)

   	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
   Intercept	67.4	2.760952	24.41187	0.001674	55.52057	79.27943
   t	-17.2429	2.104029	-8.19516	0.014565	-26.2958	-8.18994
   t^2	2.357143	0.344046	6.851252	0.020646	0.876833	3.837452

   
   The quadratic model is f(t) = 67.4 – 17.2429*t + 2.357143* t ² , where t = 1 represents the year 1998.
3. Find \(f\left( 16 \right)\). What does your result mean in terms of the situation?

d) Find the vertex of f by hand . What does it mean in terms of the situation? Be specific.

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