A high school principal is concerned about the drop in the percentage of students who graduate ...

  

A high school principal is concerned about the drop in the percentage of students who graduate from her school, show in the following table.

  

Years entered school (t)

1989

1992

1995

1998

2001

 

Percent graduating (P)

62.4

54.1

48.0

43.5

41.8

a) Estimate dP/dt for each of the three-year intervals between 1989 and 2001.

b) Does d2P/dt2 appear to be positive or negative between 1989 and 2001?

c) Explain why the values of P and dP/dt are troublesome to the principal.

d) Explain why the sign of d2P/dt2 and the magnitude of dP/dt in the year 1998 may give the principal some cause for optimism.