2 A high school principal is concerned about the drop in the

2. A high school principal is concerned about the drop in the percentage of students who graduate from her school, shown in the table below, compared with the decrease in the national average from 69.2% in 2006 to 68.8% in 2007. Year entered school, t 1995 1998 2001 2004 2007 Percent graduating, P 62.4 54.1 48.0 43.5 41.8

Solution

1995-998

dP/dt = (54.1 – 62.4)/3 = -2.77% per year

1998-2001

dP/dt = (48 – 54.1)/3 = -2.03% per year

2001-04

dP/dt = (43.5 – 48)/3 = -1.5% per year

2004-2007

dP/dt = (41.8 – 43.5)/3 = -0.57% per year

(b) Since the values of dP/dt are increasing over the whole period, d^2P/dt^2 is positive over the whole period.