Question

Assume the carrying capacity of the earth is 13 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. How does the predicted growth rate compare to the actual growth rate of about 1.2​% per​ year?

Answer 1

Answer:

The predicted growth rate is compared at  -2%

Explanation:

To calculate growth rate, G.R = X($1-\frac{Population}{Carrying capacity of earth}$)

In the 1960s,

The carrying capacity of the earth = 13 billion

Earth's population = 3 billion

X = $\frac{(Growth rate in 1960)}{(1-\frac{Population in 1960}{Carrying Capacity in 1960}) }$

X = $0.021 (1-\frac{3,000,000,000}{13,000,000,000} )$

X = 0.021 × 0.77

X = 0.01617 = 1.6%

Current population calculation:

Growth Current population (C.p) = $0.016(1-\frac{current population}{current capacity})$

Growth Current population (C.p) = 0.016$(1 - \frac{6,800,000,000}{3,000,000,000} )$

Growth Current population (C.p) = 0.016(-1.267)

Growth rate = -0.020272 = -2%

The predicted growth rate compare to the actual growth rate of about 1.2​% per​ year at -2%.