Assignment 1: Discussion—Population Growth

(For this assignment, use the Declare of Ohio population figures)

Assignment 1: Discussion—Population Growth

To deduce the development of a population mathematically, we use the concept of advocateial models. Generally telling, if we lack to forebode the acception in the population at a established conclusion in date, we set-on-foot by because the popular population and dedicate an antecedent annual development blame. For in, if the U.S. population in 2008 was 301 pet and the annual development blame was 0.9%, what would be the population in the year 2050? To clear-up this gist, we would use the forthcoming formula:

P(1 + r)n

In this formula, P represents the moderebuke population we are because, r represents the annual development blame developed as a decimal and n is the enumerebuke of years of development. In this in, P = 301,000,000, r = 0.9% = 0.009 (bear-in-mind that you must part-among by 100 to change from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we perceive:

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

Let’s deduce the aspect where we lack to perceive out when the population succeed inclose. Let’s use this identical in, but this date we lack to perceive out when the doubling in population succeed betide magnificent the identical annual development blame. We’ll set up the gist enjoy the forthcoming:

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

Now, we succeed part-among twain sides by 301,000,000. This succeed yield us the forthcoming:

2 = (1.009)n

To clear-up for n, we want to conjure a eespecial advocate edeclare of logarithms. If we catch the log of twain sides of this equation, we can affect advocate as shown below:

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

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

n = log 2 / log (1.009)

Using the logarithm office 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 magnificent annual development blame of 0.9 %.