Answer
$49$ months.
Work Step by Step
The given function is
$\Rightarrow f(x)=2.9\sqrt{x}+20.1$
Replace $f(x)$ with $40.4$ inches.
$\Rightarrow 40.4=2.9\sqrt{x}+20.1$
Subtract $20.1$ from both sides.
$\Rightarrow 40.4-20.1=2.9\sqrt{x}+20.1-20.1$
Simplify.
$\Rightarrow 20.3=2.9\sqrt{x}$
Divide both sides by $2.9$.
$\Rightarrow \frac{20.3}{2.9}=\frac{2.9\sqrt{x}}{2.9}$
Simplify.
$\Rightarrow 7=\sqrt{x}$
Square both sides.
$\Rightarrow 7^2=(\sqrt{x})^2$
Simplify.
$\Rightarrow 49=x$
Hence, the age is $49$ months.
