Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk to confectioner’s sugar while exposed to low heat. Your mixing tank starts with 10 fluid ounces of milk and 10 ounces of sugar. You continue adding sugar at a rate of 10 ounces per minute and milk at 1 ounce per minute, as depicted by the two equations below:
Where S represents the number of ounces of sugar, M represents the ounces of milk, and t represents the time in minutes. The ideal icing will have a ratio of 8 ounces of sugar per ounce of milk.
Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.
Part 1: Create a rational equation to represent the concentration (C) in ounces of sugar per ounce of milk.
Part 2: Find the domain of the concentration equation.
Part 3: Will we ever encounter a time where the rational equation is undefined? Explain your reasoning.
Part 4: Calculate the concentration after five minutes.
Part 5: How long does it take to reach a concentration of 8 ounces of sugar per ounce of milk?