Answer
$10$ days.
$(10,8)$.
Work Step by Step
The given function is
$\Rightarrow f(x)=\frac{5x+30}{x}$
Plug $f(x)=8$ into the given function.
$\Rightarrow 8=\frac{5x+30}{x}$
Multiply both sides by $x$.
$\Rightarrow 8x=\frac{5x+30}{x}\cdot x$
Cancel common factors.
$\Rightarrow 8x=5x+30$
Subtract $5x$ from both sides.
$\Rightarrow 8x-5x=5x+30-5x$
Simplify.
$\Rightarrow 3x=30$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{30}{3}$
Cancel common terms.
$\Rightarrow x=10$
Hence, after $10$ days the students remember $8$ words.
The point on the graph is $(10,f(10))=(10,8)$.
