The average yearly cost $C$ of higher education at public institutions in the U.S. for the academic years 1995/1996 to 2004/2005 can be modeled by $C = 30.57 t ^ { 2 } - 259.6 t + 6828,$ $6 \leq t \leq 15$ where $t$ represents the year, with $t = 6$ corresponding to the 1995/1996 school year. Use the model to predict the academic year when the average yearly cost of higher education at public institutions exceeds $7600.
A)1995/1996
B)1999/2000
C)2002/2003
D)2000/2001
E)1996/1997

Question

Quizplus · Accepted Answer

To predict the academic year when the average yearly cost exceeds $7600, we need to solve the inequality $30.57t^2 - 259.6t + 6828 > 7600$. Substituting the given values and solving for $t$ will give us the range of years where the cost is above $7600. Without explicitly solving the inequality here, we know that the model is quadratic and represents a parabola opening upwards, meaning costs increase over time. By testing the given options or understanding the trend, we can deduce that the year when costs exceed $7600 falls around the early 2000s, making 2000/2001 (D) the correct prediction based on the model's timeframe and the nature of the question.

The Average Yearly Cost CCC Of Higher Education at Public Institutions in the U

The Average Yearly Cost $C$ Of Higher Education at Public Institutions in the U