Question

Population growth: Suppose the world population today is 7 billion, and sup- pose this population grows at a constant rate of 3% per year from now on. (This rate is almost certainly much faster than the future population growth rate; the high spreadsheet program to help you with this question.) rate used here is useful for pedagogy. If you like, you can use (a) What would the population equal 100 years from now? (b) Compute the level of the population for t = 0, t = 1, t = 2, t = 10, 25, and t 50. t = a standard scale) graph of population (c) Make a versus time (on ratio scale graph (d) Now make the same on a

Answer 1

Given Information:

Current Population = P₀ =  7 billion = 7x10⁹

Growth rate = r = 3 %

Period = t = 100 years

Required Information:

(a) Population after 100 years = ?

(b) Population after t = 0, 1, 2, 10, 25, 50 years = ?

(c) Population vs time graph = ?

Explanation:

The human population growth can be modeled as an exponential growth,

$P = P_{0} e^{rt}$

where P₀ is the current population, r is the growth rate and t is the time period

(a) What would the population equal 100 years from now?

$P = 7x10^{9} e^{0.03*100}$

P = 140.6x10⁹  

(b) Compute the level of the population for t = 0, t = 1, t = 2, t = 10, 25, and t =50

t = 0

P = 7x10⁹e⁰

P = 7x10⁹  

t = 1

P = 7x10⁹e^0.03*1

P = 7.213x10⁹

t = 2

P = 7x10⁹e^0.03*2

P = 7.423x10⁹

t = 10

P = 7x10⁹e^0.03*10

P = 9.45x10⁹

t = 25

P = 7x10⁹e^0.03*25

P = 14.82x10⁹

t = 50

P = 7x10⁹e^0.03*50

P = 31.37x10⁹

(c) Make a population versus time graph

Attached as image