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:
![P(t)=Pe^{rt}](https://tex.z-dn.net/?f=P%28t%29%3DPe%5E%7Brt%7D)
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
![\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}](https://tex.z-dn.net/?f=%5CRightarrow%20e%5E%7B0.049t%7D%3D%5Cfrac%7B%2014%2C000%2C000%2C000%7D%7B%20151%2C000%7D)
Taking ln both sides
![\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7Ce%5E%7B0.049t%7D%7C%3Dln%7C%5Cfrac%7B%2014%2C000%2C000%2C000%7D%7B%20151%2C000%7D%7C)
![\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|](https://tex.z-dn.net/?f=%5CRightarrow%20%7B0.049t%7D%3Dln%7C%5Cfrac%7B%2014%2C000%2C000%2C000%7D%7B%20151%2C000%7D%7C)
![\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}](https://tex.z-dn.net/?f=%5CRightarrow%20t%7D%3D%5Cfrac%7Bln%7C%5Cfrac%7B%2014%2C000%2C000%2C000%7D%7B%20151%2C000%7D%7C%7D%7B0.049%7D)
years
There will be one person for every square yard of land after 1,892,147.588 years.