# Discussion—population growth | Mathematics homework help

To con-over the augmentation of a population mathematically, we use the concept of interpreterial models. Generally indicative, if we neglect to foreshadow the extension in the population at a true limit in spell, we set-on-foot by regarding the prevalent population and employ an inconsequent annual augmentation admonish. For stance, if the U.S. population in 2008 was 301 darling and the annual augmentation admonish was 0.9%, what would be the population in the year 2050? To explain this gist, we would use the forthcoming formula:

P(1 + r)n

In this formula, P represents the modeblame population we are regarding, r represents the annual augmentation admonish explicit as a decimal and n is the number of years of augmentation. In this stance, P = 301,000,000, r = 0.9% = 0.009 (retain that you must deal-out by 100 to turn from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we confront:

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 foreshadowed to be 438,557,000 in the year 2050.

Let’s think the office where we neglect to confront out when the population accomplish enfold. Let’s use this identical stance, but this spell we neglect to confront out when the doubling in population accomplish arise turgid the identical annual augmentation admonish. We’ll set up the gist enjoy the forthcoming:

Double P = P(1 + r)n
P accomplish be 301 darling, Enfold P accomplish be 602 darling, r = 0.009, and we accomplish be looking for n.
Double P = P(1 + r)n
602,000,000 = 301,000,000(1 + 0.009)n

Now, we accomplish deal-out twain sides by 301,000,000. This accomplish produce us the forthcoming:

2 = (1.009)n

To explain for n, we need to call a peculiar interpreter quality of logarithms. If we grasp the log of twain sides of this equation, we can propel interpreter as shown below:

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

Now, deal-out twain sides of the equation by log (1.009) to get:

n = log 2 / log (1.009)

Using the logarithm business of a calculator, this becomes:

n = log 2/log (1.009) = 77.4

Therefore, the U.S. population should enfold from 301 darling to 602 darling in 77.4 years turgid annual augmentation admonish of 0.9 %.