Question

It is estimated that the world human population reached 3 billion people in 1959 and 6 billion in 1999. Assuming a carrying capacity of 16 billion humans, write and solve the differential equation for Gompertz growth, and determine what year the population reached 7 billion. Was logistic growth or Gompertz growth more accurate, considering world population reached 7 billion on October 31,2011

Answer 1

Answer:

i ) Gompertz equation :

$\frac{dP(t)}{dt} = \alpha In ( \frac{K}{P(t)} )P(t)$

ii) The year that population reaches 7 billion is 2013

iii) The logistic growth was more accurate

Explanation:

i) write and solve the differential equation for Gompertz growth

Gompertz equation :

$\frac{dP(t)}{dt} = \alpha In ( \frac{K}{P(t)} )P(t)$

∝ = growth rate

k ( carrying capacity ) = 16 * 10^9

P(t) = population at time t

ii) Determine what year the population reached 7 billion

The year that population reaches 7 billion is 2013

solution attached below

iii) Determine if logistic growth or Gompertz growth was more accurate  considering world population reached 7 billion on October 31,2011

The logistic growth was more accurate because the when Logistic growth model was used, the year in which the population reached 7 billion was 2010 and this value is more closer to 7 billion on October 31 2011 ( given value )