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