Answer
$11$ learning trials
The point the graph: $(11,0.95)$
Work Step by Step
Replace $f(x)$ with $0.95$ in the function's formula.
$\Rightarrow 0.95=\frac{0.9x-0.4}{0.9x+0.1}$
Multiply both sides by $(0.9x+0.1)$ to clear denominators.
$\Rightarrow (0.9x+0.1)0.95=(0.9x+0.1)\cdot \frac{0.9x-0.4}{0.9x+0.1}$
Simplify.
$\Rightarrow 0.855x+0.095=0.9x-0.4$
Add $-0.855x+0.4$ to both sides.
$\Rightarrow 0.855x+0.095-0.855x+0.4=0.9x-0.4-0.855x+0.4$
Simplify.
$\Rightarrow 0.495=0.045x$
Divide both sides by $0.045$.
$\Rightarrow \frac{0.495}{0.045}=\frac{0.045x}{0.045}$
Simplify.
$\Rightarrow 11=x$
Hence, the learning trials are $11$.
The point the graph is $(11,f(11))=(11,0.95)$.
