crystalstewart11
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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 approximately ____%. The population will grow to three times its current size in approximately ______ years.

2.50%; 5.78%; 12%; 50%

18 years; 19 years; 23 years; 24 years

Respuesta :

Aliwohaish12
You can find it by the original equation
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0595*100=5.95%

3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years

Answer:

5.78%

19 years

Step-by-step explanation:

The Exponential Growth Model for  a population has the next formula:

[tex]P(t) = P_0 e^{k \times t}[/tex]  

where P(t) is the population after t years, [tex]P_0[/tex] is the initial population, i. e., when t = 0, and k is the annual rate of increase of the population.

From data we know that the original population is doubled after 12 years. Replacing in the formula we get:

[tex]2 \times P_0 = P_0 e^{k \times 12}[/tex]

[tex]2 = e^{k \times 12}[/tex]

[tex]ln 2 = k \times 12[/tex]

[tex]k = \frac{ln 2}{12}[/tex]

[tex]k = 0.0578[/tex]

or 5.78 %

If the population grows to three times its current size, then:

[tex]3 \times P_0= P_0 e^{0.0578 \times t}[/tex]

[tex]3 =e^{0.0578 \times t}[/tex]

[tex]ln 3 = 0.0578 \times t[/tex]

[tex]t = \frac{ln 3}{0.0578}[/tex]

[tex]t = 19[/tex]

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