Question

The population of a city has been increasing by 2% annually. In 2000, the population was 315,000. Predict the population of the city in 2020. Round your answer to the nearest thousand.

Answer 1

Answer:

The population of the city in 2020 is 3,839,832

Step-by-step explanation:

Given:

Population at 2000 =  315,000

Rate at which the population increases = 2%

To Find:

The Population in the city after 2020 = ?

Solution:

The population in the city after 2020 can be found by using Exponential growth function.

Exponential growth occurs when a quantity increases by the same factor

Exponential growth function is $y = a(1 + r)^t$

Where

y is the final amount

a is the initial amount

r is the rate of  increase

t is the time period.

Now substituting the values ,

In 2020 i.e., after 10 years

$y = 315000(1 + 2 \%)^{10}$

$y = 315000(1 + \frac{2}{100})^{10}$

$y = 315000(1 + 0.02)^{10}$

$y = 315000(1.02)^{10}$

$y = 315000\times 1.218$

y = 3,839,832.42