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## according to a survey, the population of a city doubled in 12 years. The annual rate of increase of the population of this city is appr

Question

according to a survey, the population of a city doubled in 12 years.

The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.

First box of answers: 2.50, 5.78, 12.0, 50.0

Second box of answers: 18, 19, 23, 24.

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Mathematics
1 year
2021-09-05T07:30:18+00:00
2021-09-05T07:30:18+00:00 2 Answers
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## Answers ( )

Answer:5.78 and 18 respectively

Answer:5.78

19

Step-by-step explanation:Let original population be, P = xGrowth in 12 years, A = 2xRate be = rTime = 12yearsFind the rate :The annual rate of increase of the population of this city is approximately 5.78.Find time in which the population becomes 3 times.That is A = 3x

P = x

R= 5.78%

[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]

The population will grow to three times its current size in approximately 19years .