A hearing aid clinic is trying to determine how many batteries to purchase. The more batteries the clinic purchases the cheaper the batteries are. However, storing the batteries costs money (in the form of renting space). The cost of ordering x boxes of batteries is given by the function C(x)=20x−20ln(x). The cost of storing x boxes of batteries is given by the equation S(x)=0.1(x−50)².
a) Write an equation that models the total cost of purchasing and storing x boxes of batteries.
Total cost: ___dollars