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

Answer:

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.

$=234876-\frac{0.5}{100} \times 234876=234876\left(1-\frac{0.5}{100}\right)$

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

$\begin{array}{l}{=234876\left(1-\frac{0.5}{100}\right)-\frac{0.5}{100} \times 234876\left(1-\frac{0.5}{100}\right)} \\\\ {=234876\left(1-\frac{0.5}{100}\right) \times\left(1-\frac{0.5}{100}\right)=234876\left(1-\frac{0.5}{100}\right)^{2}}\end{array}$

So, population after 5 years will be

$\begin{array}{l}{234876\left(1-\frac{0.5}{700}\right)^{5}=234876(1-0.005)^{5}=234876 \times 0.995^{5}} \\\\ {=234876 \times 0.97524=229062.5261}\end{array}$

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

Hence, the population of town after 5 years = 229062