It doesn’t take much effort to calculate the cost of 10 apples when we are told how much one apple costs. We are able to calculate the cost of 10 apples because the cost of one apple is fixed. It means, there is a particular mathematical relationship between the number of apples purchased and the cost.
The process of learning cannot be kept limited just to the understanding of the phenomenon. We have seen the importance of biomath in sets in biology in one of our previous article. Here we can see the sets of two entities. One set comprises the number of apples and the other set comprises the cost of the apples. Calculating the cost of apples is possible because we are able to figure out how the cost of apple changes with the number of apples and it is one of the basic application of mathematics in science.
We have defined a relationship between the set of ‘number of apples’ and the set of ‘costs of apples’. And this specific type of relationship between the two such sets is defined as FUNCTION in mathematical sciences. In mathematical sciences, a function is a rule by which certain analyses can be performed.
Functions are very essential to understand scientific processes. Functions help to predict the value of one parameter just by knowing the value of other parameters. One thing we must understand about the function is that one value is always dependent on the other. In the present case, the cost of apples is dependent on the number of apples purchased.
In the shop, we are free to choose the number of apples but we cannot decide the cost, unless and until you have exceptional bargaining skills. In mathematics, the number of apples that we are free to choose is called an independent variable. And the one we can’t choose as like the cost of apples is considered as a dependent variable. These two variables are at the core of the concept of the function.
In spectrophotometric measurement, we are free to choose the concentrations of the analytes but we can’t choose the absorbance. We can choose the specific length of the DNA fragment but not the melting temperature. While going with the cars we are free to choose the kilometers we want to travel but not the amount incurred. These examples of combinations of dependent and independent variables make the picture clear.
As we know for a specific value of the independent variable there is a fixed value of the dependent variable. Thus it’s of utmost importance to understand every relation need not be a function.
Is every relationship a mathematical function?
From the month of November, the temperature in the environment is decreasing. In this case for the particular value of independent variable i.e. month, there is a fixed value of dependent variable i.e. temperature. Can we call this relationship a function? The answer is no.
The temperature is not the function of the month of the year. The reason is that though there is a fixed temperature for a specific month of the year, the temperature is actually dependent on the environment and not the month of the year. That’s why this math and science relationship may not be called a FUNCTION.
It’s a prerequisite for a function that the value of the dependent variable can only be obtained after a mathematical operation on the independent variable or vice versa. Different assays performed in the biological research laboratory require a standard graph for the estimation of desired molecules. It is prepared by using the standard concentration of the molecules.
For example, to determine the concentration of protein in the plant seed the researcher will firstly prepare different concentrations of the standard protein and plot them on the X-axis as an independent variable. After that, he measures the values of absorbance for each concentration using a spectrophotometer and plots the value of absorbance on the Y-axis.
Now his job is to find a relationship between the two values. He defines the specific increase in the absorbance for a unit increase in the standard protein concentration and uses this relationship to find out the concentration of protein in the seed sample.
Knowingly or unknowingly in the field of research, we use a lot of function-based analysis as a part of science math. All the analytical instruments that perform different calculations have mathematical functions as a basis. That’s why for a better understanding of the scientific concepts, knowledge of functions is essential. In the next article, we will discuss the linear function in biology.
