For this case we have a function of the form:
![image](https://img.qammunity.org/2019/formulas/mathematics/middle-school/miq1xq4sgrbv0cocfp2m3x9slbrso9zo5j.png)
Where,
A: initial population
b: growth rate
x: time in years
Substituting values we have:
![image](https://img.qammunity.org/2019/formulas/business/college/ma6r3a3b13htcj1ljkni9okvoijyxcjvw5.png)
By the time there is one person for each square yard of land we have:
![image](https://img.qammunity.org/2019/formulas/business/college/2qjg76glncam2oa013wcl7i0bkfqxqyqfr.png)
From here, we clear x.
We have then:
![image](https://img.qammunity.org/2019/formulas/business/college/4owd6oxozvcpk9rfcyxlamz8un32up39t9.png)
Answer:
There will be one person for every square yard of land after:
![x = 167 years](https://img.qammunity.org/2019/formulas/business/college/bwdy03thww9zemnjsktyzjgyr8n2qdeg93.png)