Answer:
i ) Gompertz equation :
[tex]\frac{dP(t)}{dt} = \alpha In ( \frac{K}{P(t)} )P(t)[/tex]
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 :
[tex]\frac{dP(t)}{dt} = \alpha In ( \frac{K}{P(t)} )P(t)[/tex]
∝ = 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 )
