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Evaluating Exponential Functions

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Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following:

Current world population
Current U.S. population
Current growth rate of the world population
Current growth rate of the U.S. population

Starting in the current year, determine the following:

Based on current growth rates, how long will it take world population to reach exactly 7 billion? How long to reach exactly 10 billion?

Based on current growth rates, how long will it take for the U.S. population to reach exactly 300 million? How long for exactly 400 million?

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Solution Summary

This solution consists of a detailed explanation of evaluating an exponential function. It is provided in an attached Word document, and uses sources and calculations to determine the answers.

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Use the following website http://www.geohive.com/default1.aspx, we find the following

current world population: 6,589,571,013
current U.S. population: 300,795,465
The above numbers is for May 13, 2007.
Use the following websites http://en.wikipedia.org/wiki/World_population#Rate_of_increase and http://geography.about.com/od/populationgeography/a/populationgrow.htm , we find the following
Current growth rate of the world population : 1.14% per year
Current growth rate of the U.S. population: 0.6% per year.

Starting in the current year, ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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