# Discussion population growth | Mathematics homework help

To con-over the enlargement of a population mathematically, we use the concept of representativeial models. Generally expressive, if we absence to prophesy the acception in the population at a unfailing duration in date, we set-out by because the exoteric population and devote an conjectured annual enlargement trounce. For illustration, if the U.S. population in 2008 was 301 pet and the annual enlargement trounce was 0.9%, what would be the population in the year 2050? To clear-up this completion, we would use the forthcoming formula:

P(1 + r)n

In this formula, P represents the modetrounce population we are because, r represents the annual enlargement trounce developed as a decimal and n is the calculate of years of enlargement. In this illustration, P = 301,000,000, r = 0.9% = 0.009 (bear-in-mind that you must bisect by 100 to alter from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we furnish:

P(1 + r)n = 301,000,000(1 + 0.009)42
= 301,000,000(1.009)42
= 301,000,000(1.457)
= 438,557,000

Therefore, the U.S. population is prophesyed to be 438,557,000 in the year 2050.

Let’s reflect the office where we absence to furnish out when the population allure inclose. Let’s use this similar illustration, but this date we absence to furnish out when the doubling in population allure appear lofty the similar annual enlargement trounce. We’ll set up the completion affect the forthcoming:

Double P = P(1 + r)n
P allure be 301 pet, Inclose P allure be 602 pet, r = 0.009, and we allure be looking for n.
Double P = P(1 + r)n
602,000,000 = 301,000,000(1 + 0.009)n

Now, we allure bisect twain sides by 301,000,000. This allure surrender us the forthcoming:

2 = (1.009)n

To clear-up for n, we want to appeal-to a eespecial representative peculiarity of logarithms. If we catch the log of twain sides of this equation, we can impel representative as shown below:

log 2 = log (1.009)n
log 2 = n log (1.009)

Now, bisect twain sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm exercise of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should inclose from 301 pet to 602 pet in 77.4 years lofty annual enlargement trounce of 0.9 %.