Assume that it costs a company approximately \[ C(x)=676,000+160 x+0.001 x^{2} \] units What is the resulting average cost of a device? s How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ. \[ \$ \]

Step 1 ：The cost function for the company is given by \(C(x)=676,000+160 x+0.001 x^{2}\).

Step 2 ：The average cost of a device is calculated by dividing the total cost by the number of units produced. So, the average cost \(A(x)\) can be calculated as: \(A(x) = \frac{C(x)}{x}\).

Step 3 ：Substituting the given cost function into this equation, we get the average cost function as: \(A(x) = \frac{0.001x^{2} + 160x + 676000}{x}\).

Step 4 ：We can simplify this function by dividing each term by x, resulting in the simplified average cost function: \(A(x) = 0.001x + 160 + \frac{676000}{x}\).

Step 5 ：\(\boxed{A(x) = 0.001x + 160 + \frac{676000}{x}}\) is the final answer, representing the average cost of producing x units.