Question

The population of a city Increased from 22,700 to 26,300 between 2004 and 2010. Find the change

Answer 1

Answer:

The population increase by people per year at rate of 2.4 %

Step-by-step explanation:

Given in the question as

The Population of city in 2004 was 22,700

The population of city in 2010 is      26,300

Let the rate of increase of people per year is R%

So, population is increase from 2004 to 2010 i.e in 6 years

So, equation can be written as

Final population = Initial population $( 1+ \frac{Rate}{100})^{6}$

Or, 26,300         = 22,700  $( 1+ \frac{Rate}{100})^{6}$

Or, $\frac{26,300}{22,700}$ =  $( 1+ \frac{Rate}{100})^{6}$

Or, 1.158 =  $( 1+ \frac{Rate}{100})^{6}$

Or ,$(1.158)^{\frac{1}{6}}$ = 1 + $\frac{Rate}{100}$

Or , 1.024 - 1 =  $\frac{Rate}{100}$

Or,   0.024   =  $\frac{Rate}{100}$

∴ Rate = 0.024 × 100 = 2.4

Hence the population increase by people per year at the rate of 2.4%  Answer