Calculating the Growth Rate (r) for the Human Population

To calculate the growth rate (r) for the human population, we can use the exponential growth formula:

P(t) = P₀ * e^(r*t)

Where:
- P(t) is the population at time t
- P₀ is the initial population
- r is the growth rate
- e is the base of the natural logarithm (approximately equal to 2.71828)
- t is the time period

In this case, we are given that the human population was expected to double within 50 years. Let's assume the initial population (P₀) is 1.

Step 1: Calculate the Final Population
Since the population is expected to double, the final population (P(t)) would be 2 times the initial population. Therefore, P(t) = 2.

Step 2: Calculate the Growth Rate (r)
To find the growth rate (r), we need to rearrange the exponential growth formula:

r = ln(P(t) / P₀) / t

Where ln represents the natural logarithm.

Step 3: Substitute the Values and Calculate
Substituting the given values into the formula:

r = ln(2 / 1) / 50
r = ln(2) / 50
r ≈ 0.01396 (rounded to three decimal places)

Therefore, the growth rate (r) for the human population is approximately 0.014.

Explanation and Interpretation
The growth rate (r) represents the rate at which the human population is increasing over time. In this case, a growth rate of 0.014 means that the population is expected to increase by approximately 1.4% per year.

This exponential growth model assumes that the growth rate remains constant over time, which may not be entirely accurate in reality. However, it provides a simplified estimation of population growth.

It's important to note that population growth can have significant social, economic, and environmental implications. Understanding the growth rate helps us anticipate and plan for future challenges related to resources, infrastructure, and sustainability.