Population Double! Enough Trouble

Algebra Level 3

In England, with respect to the initial population each year, the death rate is $\frac{1}{46}$ and the birth rate is $\frac{1}{33}.$

If there were no emigration, how many years would it take for the population to double?

Note: Round up your answer.

The answer is 82.

2 solutions

Anand Raj
Jul 5, 2014

If X is the population at tlie beginning of the year, then the population at the end of the year is $x+\frac { x }{ 33 } -\frac { x }{ 46 } =\frac { 1531 }{ 1518 } x$ hence if n be the required number of years, ${ \left( \frac { 1531 }{ 1518 } \right) }^{ n }x=2x$ ; that is, $n(\log { 1531 } -\log { 1518 } )=\log { 2 }$ ; or $0.0037034n=0.3010300 \rightarrow n = 81.2857.$ However, because we're told to round up, the answer is $\boxed{82}$ .

but after 81 years the population is only approximately 1.995 times the original population.. so my first answer was 82 years.. i used compound interest formula by the way

Eric Escober - 6 years, 7 months ago

Thanks. I have updated the answer to 82, and simplified the question slightly.

In future, if you spot any errors with a problem, you can “report” it by selecting the “dot dot dot” menu in the lower right corner. You will get a more timely response that way.

Calvin Lin Staff - 6 years, 6 months ago

Noel Lo
May 28, 2015

The population increases by a factor of $1+\frac{1}{33} - \frac{1}{46} = 1.00856$ a year.

So we have $1.00856^n = 2$

$n = \frac{log 2}{log 1.00856} = 81.3 = \boxed{82}$ (rounded up to nearest whole number)

Population Double! Enough Trouble

The answer is 82.

2 solutions

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