Respuesta :
Answer:
P(0) = 7,917
Step-by-step explanation:
The population of the community is given by the following formula:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the initial population and r is the growth rate.
The initial population P0 has doubled in 5 years.
This means that
[tex]P(5) = 2P(0)[/tex]
Which lets us find r.
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]2P(0) = P(0)(1+r)^{5}[/tex]
[tex](1+r)^{5} = 2[/tex]
Applying the 5th root to both sides
[tex]1+r = 1.1487[/tex]
[tex]r = 0.1487[/tex]
So
[tex]P(t) = P(0)(1.1487)^{t}[/tex]
Suppose it is known that the population is 12,000 after 3 years.
With this, we find P(0)
[tex]P(t) = P(0)(1.1487)^{t}[/tex]
[tex]12000 = P(0)(1.1487)^{3}[/tex]
[tex]1.5157P(0) = 12000[/tex]
[tex]P(0) = \frac{12000}{1.5157}[/tex]
[tex]P(0) = 7917[/tex]
