Question

The population of a cit grows at a rate of 5% each year. The population in 1990 was 400,000. What would be the predicted current population? In what year would we predict the population to reach 1,000,000?

Answer 1

11 October 2008.

Explanation:

Rate of growth for n years is `P(1+5/100)^n`

The starting value of `P=400 000`, on 1 January 1990.

So we have `400000(1+5/100)^n`

So we need to determine `n` for

`400000(1+5/100)^n=1000000`

Divide both sides by `400000`

`(1+5/100)^n=5/2`

Taking logs

`n ln(105/100)=ln(5/2)`

`n=ln 2.5/ln 1.05`

`n=18.780` years progression to 3 decimal places

So the year will be `1990+18.780 = 2008.78`

The population reaches 1 million by 11 October 2008.