Question

a town has 10,000 residents in 2007. its population declines at a rate of 10 % per annum. what will be its total population in 2009?

Answer 1

Total population in 2009 will be 8100

Answer 2

Tip:

• Interest $I=PTR$

Explanation:

• Given a town has $10,000$  residents in 2007. Its population declines at a rate of $10\%$ per annum.
• We have to find its total population in 2009.

Step

Step 1 of 2:

The total population with interest rate in the year 2007 is

 

Now, we get the population in the year 2008 is $A=P+Pr=P(1+r)$

Now, we get the population in the year 2009 is $A=P(1+r)+P(1+r)r=P(1+r)(1+r)=P(1+r)^2$

Step 2 of 2:

Now, $P=10,000$

$r=-\frac{10}{100}=-0.1$  (∵ rate decreases by 10%)

So, $A=10,000(1-0.1)^2$

     $A=10,000\times0.9\times0.9=8,100$

Final Answer:

Hence, the total population in 2009 is $8,100$