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faust18 [17]
2 years ago
15

It is estimated that the world human population reached 3 billion people in 1959 and 6 billion in 1999. Assuming a carrying capa

city 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
Biology
1 answer:
kirza4 [7]2 years ago
5 0

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:

<u>i) write and solve the differential equation for Gompertz growth</u>

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

<u>ii) Determine what year the population reached 7 billion </u>

The year that population reaches 7 billion is 2013

solution attached below

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

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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