Question

A town had a population of 10,000 people. the population decreased 3% each year. what was the population 5 years later?​

Answer 1

Explanation:

Ok so after the first year we expect the population to reach 97% of it's initial population.

So 97% of 10 000 can be written as:

97/100 ×10 000=0.97×10 000=9 700

After the second year we expect the population to drop to 97% of the first year's population

So, it can be said that:

0.97×9700= 9409

Similarly after year 3,

0.97× 9409= 9126.73

Year 4,

0.97× 9126.72= 8852.9281

Year 5,

0.97× 8852.9281=8587 rounded to the nearest number

The new population would be 8587

Answer 2

8,588 people

Explanation:

We can represent this exponential decay as
`P=10000(0.97)^n` where
`n` is the number of years later:

`P=10000(0.97)^n\\\\P=10000(0.97)^5\\\\P=10000(0.8587340257)\\\\P=8587.340257\\\\P\approx8588`

Therefore, the population 5 years later will be 8,588 people