Rachel has been watching the number of alligators that live in her neighborhood. The number of alligators changes each week.n f(n)1 482 243 124 6Which 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

Answer:f(x) = 48(0.5)^n - 1 ⇒ 1st answerStep-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