Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
john hosts an art workshop on the weekends. he has an average of 14 students in each session and charges a fee of $12 per session. he estimates that for every $2 increase in the fee, the average number of students reduces by 1.
complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.
$c(x) = square x^2 + square x + square$

Explanation:

Step1: Define fee per student

Fee per student after $x$ increases: $\$12 + \$2x$

Step2: Define number of students

Number of students after $x$ increases: $14 - x$

Step3: Calculate revenue function

Revenue = (Fee per student) × (Number of students)

$$\begin{align*} c(x)&=(12+2x)(14-x)\\ &=12\times14 -12x +2x\times14 -2x\times x\\ &=168 -12x +28x -2x^2\\ &=-2x^2 +16x +168 \end{align*}$$

Answer:

$c(x) = \boldsymbol{-2}x^2 + \boldsymbol{16}x + \boldsymbol{168}$