Calculating with letters may seem strange at first, but they can be used to make mathematical models of real-life phenomena. Usually mathematical models are so complex that one variable is not enough to describe them. For example, in the global population growth model, the variables are A = population at the beginning, t = time in years, and k = growth factor. The population V at the end of t years is calculated with the formula [[$ V = Ak^t $]]​.

The growth factor k is affected by many factors such as diseases, wars, and famine. Therefore, it is difficult to assess it in advance. However, it is known that the world's population growth is slowing down, in the 1960s the growth rate was 1.02 (this means that the population grew by 2% per year) and at the end of 1990 it was 1.015. It is estimated that by 2015, the growth rate will drop to 1.01.

Example 2

Calculate the estimated population of the planet in 20 years from 6.7 billion in 2008. Calculate the estimation using first a growth factor of 1.015 and then a growth factor of 1.01.

List all the variables given in the task:
A = 6.7 billion 
k = 1.015 
t = 20 years

Place the variables in the expression and calculate the value of the expression:

[[$ V = Ak^t = \text{6.7} \cdot \text{1.015}^{20} \approx \text{9.0} $]] billion

Calculate the second estimate using a growth factor of 1.01.[[$ V = Ak^t = \text{6.7} \cdot \text{1.01}^{20} \approx \text{8.2} $]] billion

Answer: The estimated population of the planet after 20 years is 9.0 billion (growth factor 1.015) or 8.2 billion (growth factor 1.01).