Answer:
GENERAL EXPLICIT SEQUENCE IS GIVEN [tex]a_n = (14.74)(r)^{n-1)}[/tex]
Step-by-step explanation:
Let n be the number of year the data is recorded in.
a: The number of raccoons taken initially.
r: The multiplying factor
[tex]a_n[/tex] : The number of raccoon in the nth year.
As given: [tex]a_6 = 45, a_8 = 71[/tex]
Now, as the given situation can be expressed as GEOMETRIC SERIES:
[tex]a_n = a r^{(n-1)}[/tex]
Applying the same to given terms, we get:
[tex]a_6 = a r^{(6-1)} = ar^5 = 45\\\implies ar^5 = 45[/tex]
[tex]a_8 = a r^{(8-1)} = ar^7 =71\\\implies ar^7 = 71[/tex]
Dividing both equations, we get:
[tex]\frac{ar^7}{ar^5} = \frac{71}{45} \\\implies r^2 = 1.58\\\implies r = 1.25[/tex]
So, the first term [tex]a = \frac{45}{(1.25)^5} = 14 .74 \approx 15[/tex]
So, the GENERAL EXPLICIT SEQUENCE IS GIVEN as: [tex]a_n = (14.74)(r)^{n-1)}[/tex]
