Question

2. Calculate the intrinsic growth rate of the human population assuming that it will double over a period of 50 years. If the size of the population in 1993 was 5.4 'billion' (five thousand four hundred million), project the population for 2010. Based on your results compare the real data of the human population in 2010 (6.9 billion).

Answer 1

The population growth between t and t+1 can be modeled as:

N_t2 = N_t1 * => N_t2 / N_{t1 =}   

=> = log( N_t2 / N_{t1 )} (where, is the intrinsic growth rate we need to populate)

Given N_t2 / N_t1 = 2, and t2 - t1 = 50, we get

* 50 = log 2 = 0.301 => = 0.00602

Population in 2010 = N_t2 = N_t1 * (where N_t1 is the population in 5.4 billion)

= 5.4 * 1.01776 = 5.982

The real data of human population in 2010 (6.9 billion) is clearly more than the predicted value of 5.982 billion above, hence the model seems to underpredict the population over a period of time.