$[3\mathrm{.}63$ Points$]$

Research has shown that the relationship between the price of a cup of coffee, $p$ in dollars, and the demand, $x$ in number of cups sold $($per day$),$ is

$p=6-0\mathrm{.}1x$

The Elasticity of Demand can be written as a formula

$E(p)=-\frac{pf(p)}{f(p)}$

Where $E(p)$ is the elasticity, $p$ is the unit price, and $x=f(p)$ is the demand.

a$.$ Find the elasticity of demand formula for a cup of coffee.

$E(p)=$

b$.$ Use the elasticity of demand formula to fill out the following table.

$\backslash$table$[[$Price of cup of coffee,$\backslash$table$[[$Elasticity of$],[$Demand$]],$The price is $...,$Interpretation: If the price is increased by $10\%$dots