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

The predicted growth rate is compared at -2%

Step-by-step explanation:

To calculate growth rate, G.R = X(
`1-(Population)/(Carrying capacity of earth)`)

In the 1960s,

The carrying capacity of the earth = 13 billion

Earth's population = 3 billion

X =
`((Growth rate in 1960))/((1-(Population in 1960)/(Carrying Capacity in 1960)) )`

X =
`0.021 (1-(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-(current population)/(current capacity))`

Growth Current population (C.p) = 0.016
`(1 - (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%.