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
Answers
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 )
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