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
2 answers:
Answer:
5.78%
19 years
Step-by-step explanation:
The Exponential Growth Model for a population has the next formula:
where P(t) is the population after t years, 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:
or 5.78 %
If the population grows to three times its current size, then:
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
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Hope it helped!