Answer
$15$ days.
$(15,7)$.
Work Step by Step
The given function is
$\Rightarrow f(x)=\frac{5x+30}{x}$
Plug $f(x)=7$ into the given function.
$\Rightarrow 7=\frac{5x+30}{x}$
Multiply both sides by $x$.
$\Rightarrow 7x=\frac{5x+30}{x}\cdot x$
Cancel common factors.
$\Rightarrow 7x=5x+30$
Subtract $5x$ from both sides.
$\Rightarrow 7x-5x=5x+30-5x$
Simplify.
$\Rightarrow 2x=30$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{30}{2}$
Cancel common factors.
$\Rightarrow x=15$
Hence, after $15$ days the students remember $7$ words.
The point on the graph is $(15,f(15))=(15,7)$.
