Respuesta :
As the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year and according to that it will take 63.36 years to double the population.
A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.
According to the question:
We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.
A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.
P(t) = [tex](1.011)^{t}[/tex]
⇒ [tex]7.1[/tex] × [tex]2 = 7.1 (1.011^{t}[/tex]
⇒ [tex]\frac{7.1 * 2}{7.1} = 1.011^{t}[/tex]
⇒ [tex]1.011^{t}[/tex] = 2
Now let us solve for t using logarithm.
[tex]ln(2) = ln(1.011)^{t}[/tex]
⇒ ln(2) = t . ln(1.011)
⇒ 0.6931471805599 = t × 0.0109399400383
⇒ t = 0.0109399400383/ 0.6931471805599
⇒ t = 63.3593217
⇒ t ≈ 63.36
Therefore, it will take 63.36 years the population to be double.
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