Question

Country A has an exponential growth rate of 3.9% per year. The population is currently 5,391,000, and the land area of Country A is 40,000,000,000 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 367 year(s).
(Round to the nearest integer.)

Answer 1

The population will reach one person for every square yard of land in approximately 367 years.

Step-by-step explanation:

To find out how long it will take for there to be one person for every square yard of land, we need to determine the population when there are 40,000,000,000 square yards of land. We can use the exponential growth formula:

P = P0 * (1 + r)t

Where:

• P is the population at time t
• P0 is the initial population (5,391,000)
• r is the growth rate (0.039)
• t is the time in years

We want to find the value of t when P = 40,000,000,000. Substituting the known values into the formula, we have:

40,000,000,000 = 5,391,000 * (1 + 0.039)t

To solve for t, we can take the logarithm of both sides:

log(40,000,000,000) = log(5,391,000 * (1 + 0.039)t)

t * log(1 + 0.039) = log(40,000,000,000 / 5,391,000)

t = log(40,000,000,000 / 5,391,000) / log(1 + 0.039)

Using a calculator, we find that t ≈ 367 years.