Country A has a growth rate of 4.7% per year. The population is currently 5,646,000 and the land area of Country A is 13,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
This will happen in how many years.
(Round to the nearest integer.)
Thank you!
5646000 * 1.047^n = 13000000000
To determine how long it will take for there to be one person for every square yard of land in Country A, we need to calculate the future population and compare it to the land area.
First, let's calculate the final population. We can use the formula for exponential growth:
P = P0 * (1 + r)^t
Where:
P = final population
P0 = initial population
r = growth rate
t = time in years
Given that the initial population is 5,646,000 and the growth rate is 4.7% (or 0.047), we can rewrite the formula as follows:
P = 5,646,000 * (1 + 0.047)^t
Now, let's calculate the final population when there is one person for every square yard of land. The land area is given in square yards as 13,000,000,000. So:
Final population = 13,000,000,000
Now we can set up the equation:
13,000,000,000 = 5,646,000 * (1 + 0.047)^t
To solve for t (the time in years), we need to isolate the variable t.
Divide both sides by 5,646,000:
(1 + 0.047)^t = 13,000,000,000 / 5,646,000
Simplify the right side:
(1 + 0.047)^t = 2300
Now take the natural logarithm (ln) of both sides:
ln((1 + 0.047)^t) = ln(2300)
Apply the power rule of logarithms:
t * ln(1 + 0.047) = ln(2300)
Divide both sides by ln(1 + 0.047):
t = ln(2300) / ln(1 + 0.047)
Using a calculator, we find that ln(2300) ≈ 7.741. And ln(1 + 0.047) ≈ 0.046.
Now divide the two logarithmic values:
t ≈ 7.741 / 0.046
t ≈ 168.478
To round to the nearest integer, we get approximately 168 years.
Therefore, it will take about 168 years for there to be one person for every square yard of land in Country A.