Answer :
Answer:
current population growth rate would be -3.1%
Step-by-step explanation:
We have to:
Growth rate = r * (1 - population / carrying capacity)
for 1960,
we have carrying capacity = 21 billion
population = 3 billion
r = Growth rate 1960 / (1 - population / carrying capacity)
replacing:
r = 0.021 / (1 - 3/21)
r = 0.0245
that is to say r = 2.45%
Now the current population would be:
= 0.0245 * (1 - carrying population / carrying capacity)
we replace:
= 0.0245 * (1 - 6.8 / 3)
= -0.031
current population growth rate would be -3.1%
The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.
Given :
- Assume the carrying capacity of the earth is 21 billion.
- Use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model.
- Assume a current population of 6.8 billion.
The growth rate is given by the formula:
[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]
Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).
[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]
[tex]0.021=r\times \dfrac{18}{21}[/tex]
0.0245 = r
So, r = 2.45%.
Now, the growth rate of the current population is:
[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]
[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]
0.031 = Growth Rate
So, the growth rate is -3.1%.
For more information, refer to the link given below:
https://brainly.com/question/2096984