In this formula, P represents the initial pwth. I

In this formula, P represents the initial population we are considering, r represents the annual growth rate expressed as a decimal and n is the number of years of growth. ITo study the growth of a population mathematically, we use the concept of exponential models. Generally speaking, if we want to predict the increase in the population at a certain period in time, we start by considering the current population and apply an assumed annual growth rate. For example, if the U.S. population in 2008 was 301 million and the annual growth rate was 0.9%, what would be the population in the year 2050? To solve this problem, we would use the following formula:

P(1 + r)n 

In this formula, P represents the initial population we are considering, r represents the annual growth rate expressed as a decimal and n is the number of years of growth. In this example, P = 301,000,000, r = 0.9% = 0.009 (remember that you must divide by 100 to convert from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we find:

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

Let’s consider the situation where we want to find out when the population will double. Let’s use this same example, but this time we want to find out when the doubling in population will occur assuming the same annual growth rate. We’ll set up the problem like the following: