Final Answer:
The demand function for the "Fotim" hot dog is given by p = 5 - tan(x), where x ranges from 5 to 500.
Step-by-step explanation:
The demand function, p = 5 - tan(x), represents the relationship between the price of the "Fotim" hot dog (p) and the quantity demanded as a function of the angle x. The function p = 5 - tan(x) indicates an inverse relationship between the price and demand, where as the price increases (as x increases), the quantity demanded decreases due to the tangent function's behavior.
The range of x from 5 to 500 suggests that the demand function is evaluated for values of x within this range. As x represents an angle in trigonometric terms, the demand function implies that the quantity demanded varies as the angle x changes within this range. Notably, the tangent function fluctuates between positive and negative values based on x's position in the unit circle, signifying oscillations in the demand due to variations in price.
Understanding this demand function aids in analyzing how changes in the price (x) affect the quantity demanded for the "Fotim" hot dog. As x increases within the defined range, the demand (p) decreases due to the nature of the tangent function, emphasizing the inverse relationship between price and quantity demanded. The given function serves as a mathematical representation illustrating how price influences consumer demand for the product within the specified range of x values.