Respuesta :
Explanation:
we know population growth is an exponential phenomenon. Therefore, the sequence formed will be a geometric sequence. If P_0 is the first term and P_1 is the successive term, then we get:
[tex]P_1=P_0(1+r)[/tex]where r is the common ratio or the growth rate. Applying the data of the problem to the previous equation, we get:
[tex]781=200(1+r)[/tex]this is equivalent to:
[tex]781\text{ = 200 +200r}[/tex]solving for 200r, we get:
[tex]200r\text{ = 781 -200=581}[/tex]solving for r, we obtain:
[tex]r=\frac{581}{200}=2.9[/tex]Now, if the population grows exponentially, this trend can be modeled using the following formula:
[tex]P(t)=P_0(1+r)^t[/tex]Applying the obtained r value and the data of the problem to the previous equation, we get:
[tex]P(t)=200(1+2.9)^t[/tex]this is equivalent to:
[tex]P(t)=200(3.9)^t[/tex]with this formula, we can calculate the number of wolves in 10 years:
[tex]P(10)=200(3.9)^{10}=162808121.7[/tex]Now, if the population grows to 1000 wolves, we get the following equation:
[tex]1000=200(3.9)^t[/tex]Solving for t, we get:
[tex]t=\text{ 1.18}\approx1.2\text{ years}[/tex]We can conclude that the correct answer is:
