Final answer:
The function describing the total cost is linear, as it includes an initial fixed cost increased by a percentage plus a fixed variable cost per additional item produced. option (A)
Step-by-step explanation:
The question asks to classify the type of function that describes the total cost based on the information provided. The initial cost is $8200, which increases by 6%, and there is an additional $9.75 for each item produced. This setup indicates a starting value (the $8200 increased by 6%) and an added constant amount per item, which suggests a linear relationship between the number of items produced and the total cost.
A linear function is characterized by a constant rate of change, in this case, $9.75 per additional item. This differs from quadratic, exponential, and logarithmic functions where the rate of change itself changes as the input changes. Since the cost increases by a fixed amount per item, we can conclude that the cost function is linear.