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

The rate at which the population decrease is 59.8 %

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-(Rate)/(100))^(Time)`

Or, 22,46,000 = 30,31,000 ×
`(1-(Rate)/(100))^(50)`

Or,
`(2246000)/(3031000)` =
`(1-(Rate)/(100))^(50)`

Or,
`(2246)/(3031)` =
`(1-(Rate)/(100))^(50)`

`((2246)/(3031))^{(1)/(50)}` =
`( 1-(Rate)/(100))`

So , 0.99402 =
`( 1-(Rate)/(100))`

Or,
`(Rate)/(100)` = 1 - 0.99402

So, Rate =
`5.98* 10^(-3)` × 100

Or, Rate = 0.598 = 59.8 %

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