Answer:
f(n) = 14.3908 * 1.2561^(n-1)
Step-by-step explanation:
A geometric sequence can be defined by:
f(n) = a*r^(n-1), where 'a' is the inicial population, and 'r' is the ratio the population increases each year
If we have 45 raccoons after 6 years and 71 raccoons after 8 years, we can use these values in the equation to find the values of 'a' and 'r':
for n=6, f(n) = 45:
45 = a*r^5
for n=8, f(n) = 71:
71 = a*r^7
dividing the second equation by the first, we have:
r^2 = 71/45 = 1.5778
r = 1.2561
Now, applying this value of 'r' in the first equation, we find 'a':
45 = a*1.2561^5
a = 45/3.1270 = 14.3908
So, the function that models the local raccoon population 'f(n)' in the terms of the number of years 'n' is:
f(n) = 14.3908 * 1.2561^(n-1)
