Question

The world population is estimated to be 7.8 billion in 2020, and growing at an instantaneous rate of 1.05%. (a) Estimate the population in 2100 if the growth rate remains constant at 1.05%. (b) Estimate the population in 2100 using the logistic function, assuming a carrying capacity of 13 billion. Also, what will be the growth rate in 2100

Answer 1

Answer:

Population in 2100 is 17.99 billion.

Step-by-step explanation:

The population of the world in 2020  = 7.8 billion.

The growth rate = 1.05%

Now find the population after 2100. Use the below formula to find the population.

Population in 2100 = Population of 2020 (1 + growth rate)^n

Population in 2100 = 7.8 (1 + 0.0105)^80

Population in 2100 = 17.99 billions.

Now, find the growth rate in 2100.

dN/dt = [r N (K – N) ] / K

r = Malthusian parameter

K = carrying capacity.

Now divide both sides by K, now x = N/K then do the differential equation.

dx/dt = r x ( 1- x)

Now integrate, x(t) = 1/ [ 1 + (1/x – 1) c^-rt

From the first equation = dN/dt = (13 – 7.8) / 80 = (r × 7.8×(13 – 7.8) / 12

0.065 = (r × 7.8× 5.2) / 12

0.065 = r × 3.38

r = 1.92%