The cool company determines that the supply function for its basic air conditioning unit is s(p) = 40 + 0.008p^3 and that its demand function is d(p) = 200 - 0.16p^2, where p is the price. determine the price for which the supply equals the demand.

In this item, we are to determine the price to which there would be a breakeven between the supply and demand. This can be done by equating the equations given for each as shown below.
       S(p) = D(p)
     40 + 0.008p³ = 200 - 0.16p²

We transpose all the terms to left side of the equation. 
     0.008p³ + 0.16p² - 160 = 0
Then, we factor out the given function. This can either be done through long division or synthetic division. Divide the equation by 0.008.
        p³ + 20p² - 20000 = 0

One of the roots of the equation is 21.86. This is the only real root of the equation and the rest are imaginary. 

Hence, the price should be approximately $21.86 before the demand and supply is breakeven. 

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.