Question

Country a has a growth rate of 4.7​% per year. the population is currently 4 comma 671​,000, and the land area of country a is 10​,000,000,000 square yards. assuming this growth rate continues and is​ exponential, after how long will there be one person for every square yard of​ land?

Answer 1

For this case we have a function of the form:

$y = A * (b) ^ x$

Where,

A: initial population

b: growth rate

x: time in years

Substituting values we have:

$y = (4,671,000) * (1,047) ^ x$

By the time there is one person for each square yard of land we have:

$10,000,000,000 = (4,671,000) * (1,047) ^ x$

From here, we clear x.

We have then:

$(1,047) ^ x = (10000000000) / (4671000)\\(1,047) ^ x = 2140.9\\log1.047 ((1.047) ^ x) = log1.047 (2140.9)\\x = 167 years$

Answer:

There will be one person for every square yard of land after:

$x = 167 years$