Country A has a growt rate of 2.3% per year. The population is currently 4,435,000 and the land area of Country A is 25,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will their be 1 person for every square yard of land. Can anybody help me with this question. The answer is in the unit of years.
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25000000000=4435000e^.023x
5626.98=e^.023x
8.6371=.023x
x=375.5
5626.98=e^.023x
8.6371=.023x
x=375.5
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THis is an exponential growth problem with the formula:
x = xo * (1 + r)^t
x = 25,000,000,000
xo = 4,435,000
r = .023
t = the amount of time, which is what we are trying to figure out so:
25000000000 = 4435000(1.023)^t
divide both sides by 4435000
5637 = (1.023)^t
take the logarithm of both sides:
log(5637) = log(1.023)^t
log(5637) = t * log(1.023)
t = log(5637)/log(1.023)
t = 380 years
x = xo * (1 + r)^t
x = 25,000,000,000
xo = 4,435,000
r = .023
t = the amount of time, which is what we are trying to figure out so:
25000000000 = 4435000(1.023)^t
divide both sides by 4435000
5637 = (1.023)^t
take the logarithm of both sides:
log(5637) = log(1.023)^t
log(5637) = t * log(1.023)
t = log(5637)/log(1.023)
t = 380 years