For this case we have a function of the form:
[tex] y = A * (b) ^ x
[/tex]
Where,
A: initial population
b: growth rate
x: time in years
Substituting values we have:
[tex] y = (4,671,000) * (1,047) ^ x
[/tex]
By the time there is one person for each square yard of land we have:
[tex] 10,000,000,000 = (4,671,000) * (1,047) ^ x
[/tex]
From here, we clear x.
We have then:
[tex] (1,047) ^ x = (10000000000) / (4671000)
(1,047) ^ x = 2140.9
log1.047 ((1.047) ^ x) = log1.047 (2140.9)
x = 167 years
[/tex]
Answer:
There will be one person for every square yard of land after:
[tex] x = 167 years [/tex]
