Answer
The age groups expected are 72 and 19. This is not as accurate as the previous exercise when compared with the values in the graph, which suggests that the model proposed becomes less useful as $N$ increases.
Work Step by Step
When $N = 10$, we get the following: $$(10) = 0.013x^2 - 1.19x + 28.24$$ $$0 = 0.013x^2 - 1.19x + 28.24 - 10$$ $$0 = 0.013x^2 - 1.19x + 18.24$$ which is a quadratic equation that can be solved by using the Quadratic Formula $x = \frac{-b\frac{+}{} \sqrt {b^2-4ac}}{2a}$: $$x = \frac{-(-1.19)\frac{+}{} \sqrt {(-1.19)^2-4(0.013)(18.24)}}{2(0.013)}$$
$$x = \frac{1.19\frac{+}{} \sqrt {0.46762}}{0.026}$$
$$x \approx \frac{1.19\frac{+}{} 0.6838}{0.026}$$
$$x \approx 72$$ $$and$$ $$x \approx 19.5$$
