Glazed Icing Rational Algebraic Expressions

Glazed Icing Rational Algebraic Expressions

Part 1

We are given the sugar content, S, in ounces as a function of the time t, in minutes by S= 10+ 10t, and we are given the milk content, M, in ounces as a function of the t, in minutes as M=10 + 1t. Therefore, the concentration of sugar in milk will be given by:

This is the rational equation representing the concentration of sugar per ounce of milk.

Part 2

As provided in the problem, the time variable given by t cannot have a negative value. Therefore, any given non-negative denominator of the rational equation constructed is non-zero, meaning the domain of the equation will be given by t ≥0.

Part 3

When t= -10, the rational equation developed in Part 1 will be undefined because its denominator will be zero. Since we cannot have a negative value for time, it means it is not possible to have an undefined rational equation, and it is not possible to reach a point where the rational equation will be undefined.

Part 4

The concentration after five minutes will be given by substitution t with 5 in the rational equation as given below:

Thus, the concentration will be 4 ounces of sugar per ounce of milk after 5 minutes.

Part 5

The time taken before reaching a concentration of 8 ounces of sugar per ounce of milk will be given by;

Thus, a target concentration of 8 ounces will be reached per ounce of milk after 35 minutes.

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Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk with 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:

Glazed Icing Rational Algebraic Expressions

S equals 10 plus 10 t

M equals 10 plus 1 t

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.

Assessment Instructions
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 eight minutes.

Part 5: How long does it take to reach a concentration of 7 ounces of sugar per ounce of milk?