Developing an Equation from Average Costs

The Desert Dog and Cat Hotel is a pet hotel located in Las Vegas. Assume that in March, when dog$-$days $($occupancy$)$ were at an annual low of $500,$ the average cost per dog$-$day was $$22.$ In July, when dog$-$days were at a capacity level of $4,500,$ the average cost per dog$-$day was $$8.$

$($a$)$ Develop an equation for monthly operating costs. $($Let X $=$ dog$-$days per month$)$

Total cost $=$ Answer $1+$ Answer $2*$ X $$

$($b$)$ Determine the average cost per dog$-$day at an annual volume of $24,000$ dog$-$days. $($Round to the nearest cent.$)$