Answered

The number T of teams that have participated in a robot-building competition for high-school students over a recent period of time x(in years) can be modeled by T(x) = 17.155x^2 + 193.68x + 235.81, 0 ≤ x ≤ 6.

After how many years is the number of teams greater than 1000? Justify your answer.

Answer :

Solving the quadratic equation, it is found that the number of teams is greater than 1000 after 3.1 years.

The number of teams after x years is given by:

[tex]T(x) = 17.155x^2 + 193.68x + 235.81[/tex]

Initially, there are T(0) = 236 teams. If will 1000 be when T(x) = 1000, thus:

[tex]17.155x^2 + 193.68x + 235.81 = 1000[/tex]

[tex]17.155x^2 + 193.68x - 764.19 = 0[/tex]

Which has coefficients [tex]a = 17.155, b = 193.68, c = -764.19[/tex], then:

[tex]\Delta = (193.68)^2 - 4(17.155)(-764.19) = 89950.66[/tex]

[tex]x_{1} = \frac{-193.68 + \sqrt{89950.66}}{2(17.155)} = 3.1[/tex]

[tex]x_{2} = \frac{-193.68 - \sqrt{89950.66}}{2(17.155)} = -14.3[/tex]  

We want the positive root, so the number of teams is greater than 1000 after 3.1 years.

A similar problem is given at https://brainly.com/question/10489198

Other Questions