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mestny [16]
3 years ago
15

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

Mathematics
2 answers:
Ket [755]3 years ago
8 0

Answer:

5.78 and 18 respectively

Sergeeva-Olga [200]3 years ago
5 0

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

<u>Find the rate :</u>

   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.

<em><u>Find  time in which the population becomes 3 times.</u></em>

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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