Country A has a growth rate of 2.6% per year. The population is currently 5,918,000 and the land area of Country A is 11,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Thank you
5918*1.026^t = 11000000
To find out how long it will take for there to be one person for every square yard of land in Country A, we need to use the population growth rate and the current population and land area.
First, let's convert the land area from square yards to square miles, as follows:
Land Area = 11,000,000,000 square yards = (11,000,000,000 square yards) / (3,097,600 square yards per square mile) = 3,552.9 square miles.
Next, we need to calculate the population after a certain number of years using the exponential growth formula:
P(t) = P(0) * e^(rt),
where:
P(t) is the population after time t,
P(0) is the initial population,
r is the growth rate, and
t is the number of years.
Let's denote the time it takes for there to be one person for every square yard of land as T.
So, P(t) = 1 person per square yard, P(0) = 5,918,000, and r = 2.6% = 0.026.
We can rewrite the formula as 1 = 5,918,000 * e^(0.026T).
Dividing both sides by 5,918,000, we get e^(0.026T) = 1 / 5,918,000.
Now, let's take the natural logarithm (ln) of both sides to solve for T:
ln(e^(0.026T)) = ln(1/5,918,000),
0.026T = ln(1/5,918,000).
Now divide both sides of the equation by 0.026:
T = ln(1/5,918,000) / 0.026.
Using a calculator, we can find T to be approximately 530.06 years.
Therefore, it will take approximately 530.06 years for there to be one person for every square yard of land in Country A, assuming the current growth rate continues and is exponential.