Question

Barry has been watching the geese that live in his neighborhood. The number of geese changes each week. n f(n) 1 56 2 28 3 14 4 7 Which function best shows the relationship between n and f(n)? f(n) = 28(0.5)n f(n) = 56(0.5)n−1 f(n) = 56(0.5)n f(n) = 112(0.5)n−1

Answer 1

B. f(n) = 56(0.5)^n-1

Explanation:

First, You have to find out the starting population, if you look at the problem you see the population starts at 56

f(x) = 56

Second, you know that the population goes down 50% each week so it has a decay of 0.5

f(x) = 56(0.5)

Third, you need to add the exponent of n to make it exponential. But, if you just add n then the the population would be 28 on week 1 which is incorrect. To fix that you make the exponent n-1 so when you are on week 1 it doesn't become 28 but it stays on 56, and on week 2 it's 28, ect

f(x) = 56(0.5)^n-1