Question

If the population of a city is increasing at rate of 10% per year. At present the city population is 13310. What was the population of city 3 years earlier??

Answer 1

let 3 years ago the population of city be X.
the population of city is increasing every year at the rate of 10%.
present population of city is 13310.
the value of X

Answer 2

The population 3 years ago is 10000

Solution:

Given that,

The population of a city is increasing at rate of 10% per year

At present the city population is 13310

To find: Population before 3 years

The formula used is:

$y = a(1+r)^t$

Where, a is the initial value

y is the future value

r is the growth rate in decimal

t is the number of years

Let the population 3 years ago be "a"

$r = 10 \% = \frac{10}{100} = 0.1$

Then,

$13310 = a(1 + 0.10)^3\\\\13310 = a(1.1)^3\\\\13310 = 1.331 \times a\\\\a = \frac{13310}{1.331}\\\\a = 10000$

Thus the population 3 years ago is 10000

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