SOLUTION: 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. A

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): You can put this solution on YOUR website!
FP = PP*(1.1)^y
FP = 2*PP
2PP = PP*1.1^y
2 = 1.1^y
log(2) = y*log(1.1)
y = log(2)/log(1.1)
y =~ 7.27 years

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