With an initial population of 1,000 and a growth rate of 3%, a population increases to 1,162 after 5 years, to 1,350 after 10 years, and to 1,568 after 15 years. Did the population grow by the same number over each five-year span? If your answer is no, describe the pattern of increase.

Question

Mathematics

Nadia Marsh

Today, 19:02

With an initial population of 1,000 and a growth rate of 3%, a population increases to 1,162 after 5 years, to 1,350 after 10 years, and to 1,568 after 15 years. Did the population grow by the same number over each five-year span? If your answer is no, describe the pattern of increase.

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Answers (1)

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Nancy Huffman · Answer 1

An annual increase of 3.24% of the population.

Step-by-step explanation:

The population did not increase by the same number each year, because:

First 5 years:

1000 - 1162 = 162 people

Second 5 years:

1350 - 1162 = 188 people

Third 5 years:

1568 - 1350 = 218 people

What it says is that numerically the same number of people did not increase every 5 years, but if I increase by the same percentage, to calculate this percentage we divide the new people by the number that there were originally, that is to say:

First 5 years:

162/1000 = 0.162 = 16.2%

Second 5 years:

188/1162 = 0.1618 = 16.2%

Third 5 years:

218/1350 = 0.1615 = 16.2%

Which means that per year I increase by:

16.2 / 5 = 3.24%