Country A has a growth rate of 2.6% per year. The population is currently 4,069,000 and the land area of Country A is 33,000,000,000 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!
3.3E10 = 4.069E6 (1 +.026)^y
log(3.3E4 / 4.069) = y log(1.026)
To find out after how long there will be one person for every square yard of land in Country A, we can use the exponential growth formula:
P(t) = P0 * e^(r * t)
Where:
P(t) is the population at time t
P0 is the initial population (currently 4,069,000)
r is the growth rate (0.026 in this case, since 2.6% is equivalent to 0.026 decimal)
t is the time in years
We need to solve for t when the population P(t) is equal to the land area of Country A in square yards (33,000,000,000).
33,000,000,000 = 4,069,000 * e^(0.026 * t)
To solve for t, we can divide both sides of the equation by 4,069,000:
33,000,000,000 / 4,069,000 = e^(0.026 * t)
Now we can take the natural logarithm (ln) of both sides to isolate the exponential term:
ln(33,000,000,000 / 4,069,000) = 0.026 * t
Using a calculator, we find the natural logarithm of the left side to be approximately 5.465.
5.465 = 0.026 * t
Finally, divide both sides by 0.026 to solve for t:
t = 5.465 / 0.026 ≈ 210.576
Therefore, it will take approximately 211 years (rounded to the nearest integer) for there to be one person for every square yard of land in Country A.