Short Answer 
The population growth can be modeled using the formula P(t) = P‚ÄöCA e^(rt), where P(t) is the population at time t, P‚ÄöCA is the initial population, and r is the growth rate. Given a population increase of n% every 18 months, the calculations lead to n being approximately 4, indicating a growth rate of about 4% over that period.
Step 1: Understand the Population Growth Model
The population growth can be modeled using the formula for continuous growth, which is expressed as P(t) = P‚ÄöCA e^(rt). In this equation, P(t) represents the population at time t, P‚ÄöCA is the initial population, r is the growth rate in decimal form, and t is the time in years. By knowing these parameters, we can analyze how the population changes over time.
Step 2: Calculate the Growth Rate for the Given Parameters
The problem states that the population increases by n% every 18 months, which means the growth rate r can be described as r = n/100. Since 18 months is equivalent to 1.5 years, we can express the model for this specific time frame as P(1.5) = P‚ÄöCA e^(1.5r). This helps us set up our calculations for finding the specific value of n.
Step 3: Solve for n Using Doubling Time Formula
The key step involves using the relationship for doubling time in continuous growth, where r = ln(2) / t_d. By recognizing that the doubling time t_d is also 1.5 years, we substitute to find r = ln(2) / 1.5. To find n, we use the equation r = n/100, which leads to n = (100 * ln(2)) / 1.5. Upon solving, we find that n is approximately 4, corresponding to option C.