Respuesta :
Answer:
a). [tex]P_{n}=(1.35)P_{n-1}[/tex]
b). [tex]P_{n}=200(1.35)^n[/tex]
c). 4021 wolves
Step-by-step explanation:
Originally number wolves transplanted in the forest = 200
After 3 years, population of the wolves grown = 270
As we know population growth is an exponential phenomenon.
Therefore, sequence formed will be a geometric sequence.
If [tex]P_{0}[/tex] is the first term and [tex]P_{1}[/tex] is the successive term, then [tex]P_{1}=P_{0}(1+r)[/tex]
where r is the common ratio of each term.
[tex]270=200(1+r)[/tex]
(1 + r) = [tex]\frac{270}{200}[/tex]
r = 1.35 - 1
r = 0.35
a). Recursive formula for the number of wolves will be
[tex]P_{n}=P_{n-1}(1+r)[/tex]
[tex]P_{n}=P_{n-1}(1+0.35)[/tex]
[tex]P_{n}=(1.35)P_{n-1}[/tex]
b). Explicit formula of a exponential sequence is given by
[tex]P_{n}=P_{0}(1+r)^n[/tex]
[tex]P_{n}=200(1.35)^n[/tex]
c). We have to calculate the number of wolves in 10 years.
[tex]P_{n}=200(1.35)^{10}[/tex]
= 200×(20.1066)
= 4021 wolves
