You have started a successful start up company that produces eco$-$boxes. Each eco box has items that contribute to reducing pollution.

You model the monthly revenue of your business by the function

$R(x)=5x^2+5,$ the monthly cost by the function $C(x)=2x+1$ where $$ is the number of months your business has been operating. Use the equations, to answer the questions below.

Equations:

$R(x)=$ Revenue $C(x)=$ Cost

$P(x)=$ Profit $=R(x)-C(x)$

$AC(x)=$ Cost per month $=C\frac{x}{x}$

$AP(x)=$ Profit per month $=$P$($x$)/$x

Graph the revenue function, $R(x),$ and the cost function, $C(x),$ by hand and use the graphs to explain how your company is doing.

State and graph the average cost function $AC(x)$ by hand. Show all the characteristics and behaviour near asymptotes. Include labels and scale. What does this function tell you about how the monthly cost is changing?

State and graph the average profit per month $AP(x)$ function by hand or using Desmos. State all asymptotes. Include labels and scale. What does this function tell you about how the profit per month is changing?

Interpret the meaning of the horizontal asymptote in your average cost $AC(x)$ function in the context of your business idea.

What will be the monthly profit after $1$ year? Show all calculations Be sure to write the answers neatly and clearly