Answer
$15.6$ years old
Work Step by Step
$ f(x)=-2.32x^2+76.58x-559.87$
and $12 \leq x \leq 17$ ; $ f(x)=70$
$-2.32x^2+76.58x-559.87=70$
or, $2.32x^2-76.58x+629.87=0$
$ x=\dfrac{-(-76.58) \pm \sqrt {(76.58)^2-4 \times 2.32 \times 629.87}}{(2)(2.32)}$
or, $ x=\dfrac{76.58 \pm 4.3935}{4.64}$
So, $ x_1 \approx 17.5; x_2 \approx 15.6$
Because $12 \leq x \leq 17$, only the value of $ x_2$ applies.
So, $ x_2 \approx 15.6$
