Rachel has been watching the number of alligators that live in her neighborhood. the number of alligators changes each week.
n f(n)
1 48
2 24
3 12
4 6
which function best shows the relationship between n and f(n)?
f(n) = 48(0.5)^n − 1
f(n) = 48(0.5)^n
f(n) = 24(0.5)^n
f(n) = 96(0.5)^n − 1

f(x) = 48(0.5)^n - 1 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of alligators changes each week

∵ The number in week 1 is 28

∵ The number in week 2 is 24

∵ The number in week 3 is 12

∵ The number in week 4 is 6

∴ The number of alligators is halved each week

∴ The number of alligators each week = half the number of alligators

   of the previous week

- The number of alligators formed a geometric series in which the

  first term is 48 and the constant ratio is 1/2

∵ Any term in the geometric series is Un = a r^(n - 1), where a is the

  first term and r is the constant ratio

∴ f(n) = a r^(n - 1)

∵ a = 48 ⇒ The number of alligators in the first week

∵ r = 1/2 = 0.5

∴ f(x) = 48(0.5)^n - 1