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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Answers

  2. Answer:

    5.78

    19

    Step-by-step explanation:

    Let original population be, P = x

    Growth in 12 years, A = 2x

    Rate be = r

    Time = 12years

    Find the rate :

       A = P(1 + \frac{r}{100})^t

     2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%

    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%

                   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

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

         

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