Week 10 Assignment - Coursework Example

Exponential growth rate Rate Exponential Growth Rate Geometric growth rate also called exponential growth rate refers to the growth rate of a mathematical variable in relational to the functions defined by the given value (Khan, 2015). Under ideal conditions, the population of rats over time has shown an exponential growth rate which is useful in the estimating the population of rats at any specific time and their impact on the environment in addition to its usefulness in studying specific properties of the given family of rats (Khan, 2015).

Therefore, assuming that the population of rats exhibits an exponential function which is a function of time, the population of rats at any given time t is given by………… (i)Where the original population of rats at time t = 0 and r is the growth rate.ExplanationSubstituting the given original population and the growth rate into equation (i)………… (ii)Using equation (ii) above, the population of rats after one week (7 days) is given byWhich approximates to 245 rats by the end of 7 daysSimilarly, after 14 days, the population of rats is given byWhich is approximately 597 rats by the end of the 2nd week.

To estimate the time required to double the population, the above exponential growth function is used as shown with the initial population set at 200Taking logarithms both sides of the equationSo that, Conclusion In this study, the population of rats has been shown to assume an exponential growth pattern. The growth function was given as shown above which is useful in estimating the population of rats and the time a specific population shall be achieved. The population of rats after one week was approximately equal to 245 whereas after 2 weeks it was found to be 597 rats.

Thus, if the population at any given time is known then, the time required to attain such a population can be evaluated. Again, the period required to achieve doubling of the initial population was shown to be 5.44 days. This function is useful in studying the various populations in the environment, as well as are useful in solving real life problems such as projecting the possible population after a given period.ReferenceKahn, D. S. (2015). Attacking problems in logarithms and exponential functions.

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