a business has a budget of $480 to spend on their marketing campaign. each month, x, the business spends $30…

a business has a budget of $480 to spend on their marketing campaign. each month, x, the business spends $30 on different advertisements. the amount of money remaining in the budget for marketing can be modeled by the function m(x)= -30x + 480. based on the graph of the linear function m(x) and the context of the problem, what is the domain? 0, ∞ 0, 16 0, 480 ℝ

a business has a budget of $480 to spend on their marketing campaign. each month, x, the business spends $30 on different advertisements. the amount of money remaining in the budget for marketing can be modeled by the function m(x)= -30x + 480. based on the graph of the linear function m(x) and the context of the problem, what is the domain? 0, ∞ 0, 16 0, 480 ℝ

Answer

Explanation:

Step1: Determine lower - bound of domain

The number of months $x$ cannot be negative in this context. So the lower - bound of the domain is $x = 0$.

Step2: Determine upper - bound of domain

The money remaining $M(x)$ must be non - negative. Set $M(x)=0$ and solve for $x$. [ \begin{align*}

  • 30x+480&=0\ -30x&=-480\ x& = 16 \end{align*} ] When $x = 16$, the budget is completely spent. So the upper - bound of the domain is $x = 16$.

Answer:

B. $[0,16]$