Question

The population of a town is 234,876 and is decreasing at a rate of 0.5% each year.

Predict the population in 5 years (round to th nearest whole number).

Answer 1

The population of a town is 234,876. The population in 5 years is 229062

Solution:

Given, the population of a town is 234,876 and is decreasing at a rate of 0.5% each year.

We have to predict the population in 5 years (round to nearest whole number).

Now, population after 1 year = present population – 0.5% of present population.

`=234876-(0.5)/(100) * 234876=234876\left(1-(0.5)/(100)\right)`

Now, population after 2 years = population after 1 year – 0.5% of population after 1 year.

`\begin{array}{l}{=234876\left(1-(0.5)/(100)\right)-(0.5)/(100) * 234876\left(1-(0.5)/(100)\right)} \\\\ {=234876\left(1-(0.5)/(100)\right) *\left(1-(0.5)/(100)\right)=234876\left(1-(0.5)/(100)\right)^(2)}\end{array}`

So, population after 5 years will be

`\begin{array}{l}{234876\left(1-(0.5)/(700)\right)^(5)=234876(1-0.005)^(5)=234876 * 0.995^(5)} \\\\ {=234876 * 0.97524=229062.5261}\end{array}`

As persons can’t be in fractions, population after 5 years = 229062

Hence, the population of town after 5 years = 229062