Question 350855: Dear sir,
Please help me with the following question.
hope u will send the solutions at the earliest. Thank you.
1. The population of an island increases by 10% each year. After how many years will the original population be doubled?
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The formula for an increase of 10% per year would be:
f = p * 1.10^n
f = future population
p = present population
n = number of years
assume the present population is 1.
assume that the population doubles.
this makes the future population = 2.
that could be 1, 1000, 1 million, 1 billion.
doesn't matter.
the future population is two times the present population, whatever the present population is.
the formula f = p * 1.10^n therefore becomes:
2 = 1 * 1.10^n
you want to find n.
if you take the log of each side of this equation, you will get:
log(2) = log(1 * 1.10^n)
there are two laws of logarithms that apply here.
the first is log(a*b) = log(a) + log(b)
the second is log(a^b) = b*log(a)
applying those laws, your formula becomes:
log(2) = log(1) + n * log(1.10)
since log(1) = 0, this formula becomes:
log(2) = n * log(1.10)
divide both sides of this equation by log(1.10) and you get:
log(2) / log(1.10) = n
use your calculator to divide log(2) by log(1.10) and you will get:
n = 7.272540897
if that's correct, then the population will double in 7.272540897 years.
plug that value in your original equation to see if that's true.
your original equation is:
2 = 1 * 1.10^n
replace n with 7.272540897 to get:
2 = 1 * 1.10^7.272540897
solve using your calculator to get:
2 = 2
this confirms the answer is correct.
the population will double in 7.272540897 years if the annual growth rate is 10%.
Answer by Alan3354(69443)  (Show Source):
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