Question

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 1

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:

$T(x) = 17.155x^2 + 193.68x + 235.81$

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

$17.155x^2 + 193.68x + 235.81 = 1000$

$17.155x^2 + 193.68x - 764.19 = 0$

Which has coefficients $a = 17.155, b = 193.68, c = -764.19$, then:

$\Delta = (193.68)^2 - 4(17.155)(-764.19) = 89950.66$

$x_{1} = \frac{-193.68 + \sqrt{89950.66}}{2(17.155)} = 3.1$

$x_{2} = \frac{-193.68 - \sqrt{89950.66}}{2(17.155)} = -14.3$  

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

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