a) population of the town after 15 years
P(15) = 12(1.025^15)
P(15) ≈ 12(1.466096)
P(15) ≈ 17.59
The population of the town after 15 years is approximately 17,590.
b) growth rate of the town after 20 years
To find the growth rate after 20 years, we need to find the value of P(20) and then calculate the percentage increase.
P(20) = 12(1.025^20)
P(20) ≈ 12(1.485944)
P(20) ≈ 17.83
The population of the town after 20 years is approximately 17,830.
The growth rate after 20 years can be determined by calculating the percentage increase from 12,000 to 17,830.
Percentage increase = ((17,830 - 12,000) / 12,000) * 100%
Percentage increase ≈ 48.58%
The growth rate of the town after 20 years is approximately 48.58%.
A town with a population of 12 000 has been growing at an average rate of 2.5% for the last 10 years l. Suppose this growth rate will be maintained in the future. The function that models the towns growth is
P(n) = 12(1.025^n)
Determine the
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