Question

According to data from the U.S. Department of Education, the average cost y of tuition and fees at public four-year institutions in year x is approximated by the equation y=0.024x⁴-0.87x³+9.6x²+97.2x+2196 where x = 0 corresponds to 1990. If this model continues to be accurate, during what year will tuition and fees reach $4000?

Answer 1

To find the year when tuition reaches $4000, we need to solve the polynomial equation y = 0.024x^4 - 0.87x^3 + 9.6x^2 + 97.2x + 2196, where y equals 4000 and x represents years since 1990. Numerical methods or graphing would be used as the equation is complex.

Step-by-step explanation:

The question seeks to determine the year in which the average cost of tuition and fees at public four-year institutions will reach $4000 based on a given polynomial model. To find the year, we will set the equation y = 0.024x^4 - 0.87x^3 + 9.6x^2 + 97.2x + 2196 equal to 4000 and solve for x, where x represents the number of years since 1990.

This involves finding the roots of the polynomial equation 0.024x^4 - 0.87x^3 + 9.6x^2 + 97.2x + 2196 - 4000 = 0. This equation does not have a straightforward algebraic solution and would typically require numerical methods or graphing tools to solve.

Once x is determined, the year can be calculated by adding the value of x to 1990.