Problema Solution
Country A has a growth rate of 3.3% per ear. The Population is currently 5,549,000, and the land area of Country A is 20,000,000,000 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 provided by our tutors
Continuous exponential growth is described with:
P(t) = P0e^(rt), where
P0 = 5,549,000 is the initial population size.
r = 0.033 is the annual interest rate in decimal form
t = is the time in years (we need to find)
P(t) = 20,000,000,000 is the population size after t years (1 person for every square yard of land mean there will be 20,000,000,000 people)
P0e^(rt) = P(t)
5,549,000e^(0.033t) = 20,000,000,000
e^(0.033t) = 20,000,000,000/5,549,000
t = (1/0.033) ln(20,000,000,000/5,549,000)
t = 248.18 years
click here to see the step by step calculation:
after 248.18 years there will be 20,000,000,000 people or one person for every square yard of land.