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blackartbaby
09-28-2008, 07:32 PM
In 2006 the population of Mexico was 107.4 million. If Mexico's population continues to grow at an annual rate of 1.43%, then the population in 2028 will be 107.4(1.0143)(to the 14th power) million.

A) Find the predicted population in 2020 to the nearest tenth of a million people.
b) Use result of above to determine whether the United States or Mexico will have a greater increase in population between 2006 and 2020.

Denis
09-28-2008, 11:23 PM

mmm4444bot
09-29-2008, 02:51 AM
Hi Black Art:

Two things look goofy to me in this exercise. I interpret the given expression for Mexico's population after t years to be as follows.

107.4 \; (1.0143)^t

In order for this expression to equal 107.4 (the given population in Mexico in 2006), the value of t needs to be zero.

This means that t corresponds to the number of years since 2006. It also means that setting t = 14 (you typed "the 14th power" for the projected population in 2028) corresponds to the year 2020 instead of 2028.

2028 - 2006 = 22

2020 - 2006 = 14

In other words, when t = 22, then you get the projected population for the year 2028, and, when t = 14, then you get the projected population for the year 2020.

I suppose it's possible that the units on variable t are not years, and thus we could scale t = 0 to 14 to mean a span of 22 years, but that's not how these exponential models for population are usually set up. Please check the information that you were given.

Also, did you receive any information about the projected increase in population for the United States from 2006 to 2020? If not, then I do not understand how you could make a comparison in the absence of figures for the United States during the same period.

Cheers,

~ Mark :)