1. Assume initial population of 2700, rate of growth of 6%, and time interval of 15 years. The formula to be used is also called continuous growth formula . The future value is:
FV=PV×ert
PV=2700, r=0.06, t=15
FV=2700×e0.06×15=6640
2. For time intervals 30 and 45:
PV=2700, r=0.06, t=30, 45
FV=2700×e0.06×30=16334
FV=2700×e0.06×45=40175
3. For growth rates 8% and 10%:
PV=2700, r=0.08, t=15,30, 45
FV=2700×e0.08×15=8964
FV=2700×e0.08×30=29763
FV=2700×e0.08×45=98815
PV=2700, r=0.10, t=15,30, 45
FV=2700×e0.10×15=12100
FV=2700×e0.10×30=54230
FV=2700×e0.10×45=243050
The results from calculations are similar to the results coming from the Excel file.
4. The graphs are not straight lines but are curved lines. As the growth rate becomes higher, the slopes of the curved lines become steeper towards the end. The growth rate affects how fast the population increases as time goes by. A 2% increase in growth rate shows a significant difference of steepness of the curved lines.
5. The exponential growth rate shows a very troublesome trend because the increase in population is very fast. As a year passes by, the increase in population is already greater than the previous year. For a growth rate of 10%, the population increases more than 4 times in just a span of 15 years. When a population of organisms increase exponentially, the chances of survival for each individual organism becomes slim because there will be competition on available resources. Eventually, the resources from the environment will be reduced until only a few organisms will be able to access these; the organisms without access to the resources will die. If the population growth is uncontrolled, there will come a time wherein the resources will not be enough to sustain the population.
There are several environmental factors that inhibit the exponential growth rate of population of organisms. Death is the natural deterrent for this; every organism has a life span. The death of organisms can be by natural causes or old age, by accident, by disease, by predation, or other environmental causes like global warming. Because of these environmental factors,
6. Because of several natural factors, the percent growth rate of a population will not be constant over a long period of time. In particular, limitations in available resources will most likely cause a decline, or decay, in population somewhere in the middle of the timeline. The decay can be modeled by an exponential decay equation, in which the growth rate is negative. If the environmental resources become sustainable, there will again be an increase in the population. However, if the resources become depleted, this might cause extinction of the population.
References
Simmons, B. (2016, February 21). Exponential Decay. Retrieved June 22, 2016, from Math Words: http://www.mathwords.com/e/exponential_decay.htm
Stapel, E. (2012). Exponential Functions: The "Natural" Exponent "e". Retrieved June 22, 2016, from Purplemath: http://www.purplemath.com/modules/expofcns5.htm
