Exponents are used to signify a number or variable multiplied by itself several times. For example, 4^5 is four times itself five times, or 1,024. Exponents are a key feature of polynomial and exponential functions in algebra. Exponents are used in a wide variety of jobs that use these equations for statistical modeling and scientific analysis.
Scientists must use polynomial and exponential functions in their work to explain phenomena and perform statistical operations on their data. For example, scientists performing radiocarbon dating for animal fossils and other organic matter use the formula for the half life of the element carbon, which contains an exponent: A = 0.5^(t/h), where A is the final amount, t is the elapsed time and h is the element's half life (how long it takes for half of the element's atoms in a substance to decay).
Ecologists studying ecosystems rely on exponential equations in their calculations. The growth of populations is calculated using the logistical growth model, which contains exponents corresponding to the growth rate and elapsed time (see ref 2). The logistical growth model is used in situations where growth would be exponential but for environmental or other factors that come into play once the population reaches a certain level. In Ecology, these limiting factors include food scarcity and predation.
Tradesmen such as carpenters, electricians and mechanics use polynomial equations in their routine calculations. A carpenter must estimate the dimensions of areas and volumes the proper slopes for construction, relying on polynomial equations. The formula for the volume of a cylinder, for example, is 3.14 times the square of the radius of the base circle times the height of the cylinder. Electricians also use formulas with exponential terms in their calculations. For example, the formula for the watts in a circuit is equal to I^2*R, or the current squared times resistance.
Accountants have to perform hundreds of different computations on financial data, many of which involve exponents. A common example is the PERT formula for compound interest, A = P_e^(r_t), or the current amount is equal to the principal amount mutiplied by e (approximately 2.718), raised to the exponent (r times t), where "r" is the interest rate and "t" is the amount of time. For compound monthly interest, "t" would be in units of months, and for compound yearly interest, "t" would be in terms of years.
Many engineering professions use exponential and polynomial functions in their calculations. Engineers use mathematical modeling to understand and predict the behavior of complex phenomena such as wind flow or structural stress. One of the most common types of mathematical modeling relies on higher-order polynomial equations. Using higher exponents and adjusting the coefficients allows engineers to create an equation that most closely matches their data.