Chapter SH, Problem 7.26EP

To determine

To calculate number of resident in 2012.

Answer to Problem 7.26EP

The residents in 2012 were 3648.

Explanation of Solution

Given information:

The number of residents in 2006 are 4518.

The number of residents has been declining by 3.5% each year. Formula used:

  $P{\left(1-\frac{R}{100}\right)}^n$

where,

P is present population.

Population declining at rate R% per year

n is number of years

Calculation:

As from 2006 to 2012 number of years will be 6

Then, $n=6$

Substituting the value of P, R, and n in the formula to find resident in 2012.

  $=4518{\left(1-\frac{3.5}{100}\right)}^6$

On solving,

  $=4518{\left(\frac{96.5}{100}\right)}^6$

Further solving,

  $=4518{\left(0.965\right)}^6$

On solving,

  $=4518\left(0.80753\right)$

On solving,

  $\approx 3648.46$

Then, approximate final anwer is 3648.

Hence, the residents in 2012 were 3648.