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Dosage calculation is a crucial component in ensuring the proper administration of medication, such as Ivermectin for dogs. Accurate dosage makes sure that the medication is effective without causing harm. In this exercise, the function provided, \(D(x)=\frac{136}{25} x\), allows us to calculate the dosage in milligrams given a dog's weight in pounds. To find the dosage:

• Insert the dog's weight into the function for \(x\).
• Perform the arithmetic operation to determine \(D(x)\).

For example, if a dog weighs 35 pounds, substitute 35 for \(x\) and solve. This results in the computation of the specific milligram dosage required for the dog's weight.

The substitution method is a mathematical technique used to solve problems by replacing variables with specific values. This is particularly useful when working with functions, like the dosage calculation function in this example. To use substitution:

• Identify the variable to substitute, which is the dog's weight, \(x\), in the dosage formula.
• Replace \(x\) with the specific weight value.
• Calculate the numeric result using basic arithmetic operations.

This method allows for direct computation of \(D(x)\), providing the exact dosage needed. For instance, for a 70-pound dog, substituting 70 gives the correct dosage of 380 milligrams.

The weight-dosage relationship is a fundamental concept in pharmacology that ensures the effectiveness and safety of medication administration. In the case of Ivermectin for dogs, there is a direct proportional relationship between a dog's weight and the dosage required. This relationship is expressed in the function \(D(x)=\frac{136}{25} x\), where:

• \(x\) represents the weight in pounds.
• \(D(x)\) represents the dosage in milligrams.

With this linear relationship, as a dog's weight increases, the required dosage also increases proportionally. Thus, accurate weight measurement is vital for determining the proper dosage, ensuring the medication's efficacy without risking an overdose or underdose. This calculation method provides a systematic way of adjusting the dosage according to weight to meet the specific needs of each dog.