Respuesta :
Answer:
There will be one person on 1 square yard of land after 1,892,147.588 years.
Step-by-step explanation:
Continuous exponential growth formula:
[tex]P(t)=Pe^{rt}[/tex]
P(t)= Population after t years.
P= Initial population
r=rate of growth.
t= time in year
Given that,
Growth rate of country A (r)= 4.9% per year=0.049 per year.
Initial population (P)= 151,000.
Land area of country area= 14,000,000,000 square yards.
There will be one person on one square yard of land.
So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.
P(t)=14,000,000,000 person
[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]
[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]
Taking ln both sides
[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]
[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]
[tex]\Rightarrow t}=1,892,147.588[/tex] years
There will be one person for every square yard of land after 1,892,147.588 years.
