Question

Suppose the population of a certain city is 3031 thousand. It is expected to decrease to 2246 thousand in 50 years. Find the percent decrease
%
The percent decrease is approximately
(Round to the nearest tenth )

Answer 1

Answer:

The rate at which the population decrease is 59.8 %  

Step-by-step explanation:

Given as :

The population of city = 30,31,000

Now The population of city decrease to 22,46,000

The time period in which population decrease is 50 years

Let the percentage rate of decrease = R%

So,

Final population = initial population × $(1-\frac{Rate}{100})^{Time}$

Or, 22,46,000 = 30,31,000 × $(1-\frac{Rate}{100})^{50}$

Or, $\frac{2246000}{3031000}$ =  $(1-\frac{Rate}{100})^{50}$

Or, $\frac{2246}{3031}$ = $(1-\frac{Rate}{100})^{50}$

$(\frac{2246}{3031})^{\frac{1}{50}}$ = $( 1-\frac{Rate}{100})$

So , 0.99402 = $( 1-\frac{Rate}{100})$

Or,  $\frac{Rate}{100}$ = 1 - 0.99402

So, Rate = $5.98\times 10^{-3}$ × 100

Or, Rate = 0.598 = 59.8 %

Hence The rate at which the population decrease is 59.8 %  Answer