This lesson will take a look at different ways in which calculus is used in the real world. A short quiz follows that will allow you to test your knowledge about how calculus is used in our everyday lives.

## Calculus in the Real World

Oftentimes students ask, ‘When will I ever use this again in life?’ That is a fair question, as it seems most of what they learn in school has no foreseeable value in the real world.

However, many of the concepts being taught in school are used in our everyday lives in ways that we may never imagine. This is certainly the case when it comes to calculus!Isaac Newton introduced calculus as a means of studying gravity – perhaps you have even heard of Newton’s Law of Motion. Simply put, the **Law of Motion** surmises that: (1) an object will not move unless it is forced to do so; (2) the formula *F* = *ma* represents the relationship between acceleration and applied force; (3) every action has a counteraction. The Law of Motion has been extended to include other areas that Newton himself likely never considered.**Calculus** helps explain how things change over time and it is used to gather and analyze information in engineering, science, medicine and advanced mathematics.

You may be surprised that some of the most unexpected activities require complex formulas used in calculus. Chances are, every time you used your credit card, filled a prescription or pumped gasoline, a calculus formula was used to calculate it. Let’s now look at some other examples of how calculus may be used.

## Environmental Changes

Let’s say you read an article that suggests that by the year 2050 a major earthquake will cause the Earth’s crust to crack open about five miles wide. You may wonder exactly how would scientists be able to determine the approximate year in which this change will happen and the depth of the change?Scientists would first study the crust and record their observations. Perhaps the scientists first noticed signs of the Earth’s crust splitting and decided to check back in a year or so to determine whether any further splitting has taken place.

A year later, the scientists noted that the Earth split another one to two centimeters since their last observations. Using a calculus-based mathematical model, the scientists could calculate the rate and speed of change that is taking place within the Earth’s crust, thus allowing them to make a reasonable estimation that a five-mile-wide split is probable.

## Economic Forecasts

Economists use calculus to predict such things as potential earnings, stock market changes and expected business profits.

Consumers rely on such **forecasts**, or predictions, to make decisions about spending. For example, if economists expect the housing market percentage rates to increase within the next five years, a consumer may decide that buying a house now is in his or her best interest. For this reason, forecasts need to be as accurate as possible with little room for error.Credit card companies use calculus to set the minimum monthly payments based on interest rates and available balance at the time the statement is processed. Suppose there was a predicted change in the average income of middle class families this year, and that as a member of the middle class, you may be interested in finding out how much of a percentage your income will change. A simple formula that you could use is income = (Y2 – Y1) / Y2 * 100.

In other words, you would look at your old income (Y2) and subtract it from your new income (Y1). You would then divide that number by your old income (Y2) and multiply it by 100. The number 100 represents the sample population being considered as part of the equation.

## Health and Human Services

Calculus formulas are used in research to analyze and report on findings from a study, too.

For example, a study that concludes 1 in 68 children are diagnosed with autism each year would have to take into account birth dates in a given year and how many children within those perimeters were born with autism.Calculus-based formulas are also used to determine birth and death rates. For example, the formula *b* / *p* * 1,000 represents number of births (*b*) divided by total population (*p*) multiplied by 1,000. Likewise, the death rate would be construed as *d* / *p* * 1,000, representing number of deaths (*d*) divided by total population (*p*) multiplied by 1,000. Similar formulas are created for marriage, divorce, fertility and infant mortality rates. The number 1,000 represents the sample population used for the equation.In addition, a doctor needs to know how much medicine to prescribe his or her patients based upon individual factors, such as age, height and weight.

When a person takes medication, whether over-the-counter or prescribed, he or she would have to know how much is recommended based on the information provided. For example, the formula *D* / *H* * *V* represents dosage (*D*) divided by the dosage in the medicine container (*H*) times the type of medicine (*V*), meaning if it is a tablet, liquid or cream. The formula calculates exactly how much should be taken by the patient. Normally, calculations of this nature are already provided by the doctor, pharmacy or pharmaceutical company.

## Lesson Summary

Mathematical formulas associated with **calculus** are used to demonstrate changes that are expected to take place over a certain period of time. Fields like medicine, economics and geology depend on formulas to gather and organize information in order to determine certain outcomes. Although Isaac Newton originally introduced calculus as a means of explaining gravity and the **Law of Motion**, it is now used to help us make decisions that impact our daily living in ways that are both major and minor.