If a single female rabbit lived for seven years and maintained that reproduction rate, and all of the female baby rabbits started reproducing at the same rate at the age of six months… The biological limit to how fast the population of rabbits can grow is based on the gestation period, the time to maturity of the rabbits, and the average size of the litter.All of those factors can be combined mathematically to predict the growth rate of a population of rabbits over a given time period.Leftovers that sit outside the refrigerator overnight might “go bad” quickly even though they will last for several days in the refrigerator. One reason is the presence of bacteria—bacteria are everywhere, and some are good for us and some are bad for us.
Throughout the 1600s, many mathematicians in Europe were working with exponents, exploring both the mathematical concepts and the applications of those concepts in everything from astronomy to finance.
In 1683, the Swiss mathematician Jacob Bernoulli was studying the expression (1 1/.
In other words, if you wanted to maximize the interest you were paid on your investment, how frequently should that interest be calculated? If you think about this in terms of calculating interest, Bernoulli’s result shows that you don’t gain much more from calculating and paying out the interest ten times a year than you get from calculating it six times a year, and the biggest difference comes between one and three times a year.
As larger and larger values of n are substituted, the value of the expression approaches a constant, which is approximately 2.71828—the value reported by Bernoulli as the limit of the expression (Figure 2).
In science, the constant for a specific material, process, or environmental condition.
For example, most bacteria split more rapidly at room temperature than at near freezing, so the same bacteria will have a different growth rate constant even though they both decay radioactively because they are different materials.But because the two isotopes are decaying, or decreasing over time, both growth rate constants are negative – a different process than reproduction.We are often advised to refrigerate foods after opening them.This natural, continuously and gradually growing population is therefore not accurately described by an exponential equation with a base value ( has many uses in math, but in science we consider it the base rate of change (growth or decay) in systems that are continuously changing (growing or decaying) over time.Those systems might be a population of bacteria, a chemical reaction, or the decay of a radioactive material.This would be the value of the interest paid on your investment if you had a 100% interest rate and if it were paid out constantly, an infinite number of times per year.