Question

The breakdown of a sample of a chemical compound is represented by the function , where p(t) represents the number of milligrams of the substance and t represents the time, in years. in the function p(t), explain what 0.5 and 300 represent.

Answer 1

In the function p(t), the 0.5 represents the half-life of the chemical compound in years, while 300 represents the initial amount in milligrams of the substance before it starts to decompose.

Step-by-step explanation:

When discussing the function p(t) that represents the breakdown of a chemical compound, 0.5 refers to the half-life of the reaction, or the time it takes for half of the substance to decompose. 300 represents the initial milligrams of the substance before decomposition begins.

The half-life is crucial because it indicates how quickly a substance breaks down, and is a characteristic of first-order reactions. For example, if the half-life of a substance is 0.5 years, after 0.5 years, the amount will reduce to half of the initial amount.

If we start with 300 mg of the substance, after one half-life (0.5 years), we would expect to have 150 mg remaining. Understanding the concept of half-life helps in predicting how long a substance will remain effective or in what timeframe precautions need to be taken for substances that degrade into hazardous products.