between 1998 and 2004, the number of college freshman who planned to get a professional degree computer science can be reasonably modeled by
f(x)=-348.2x^2+1402x+13,679
where x=0 represenjts 1998. based on this model, in what year did the percent of freshman planning to get a computer degree reach its maximum?
for y = ax^2 + bx + c, the max or min is reached at x = -b/2a = 1402/696.4
To find the year when the percentage of college freshmen planning to get a computer science degree reach its maximum, we need to determine the vertex of the quadratic function f(x) = -348.2x^2 + 1402x + 13,679.
The vertex of a quadratic function can be found using the formula:
x = -b / (2a)
Where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c.
In our case, the equation is f(x) = -348.2x^2 + 1402x + 13,679, so the coefficients are:
a = -348.2
b = 1402
Using the formula, we can calculate x:
x = -1402 / (2 * -348.2)
x ≈ 4.02
Since x represents the number of years after 1998, we can add 4.02 to 1998 to find the year when the percentage reached its maximum:
1998 + 4.02 ≈ 2002.02
Therefore, the model suggests that the percentage of college freshmen planning to get a computer science degree reached its maximum in the year 2002.