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)? a. f(n) = 28(0.5)^n b. f(n) = 56(0.5)^n-1 c. f(n) = 56(0.5)^n d. f(n) = 112(0.5)^n-1

Answer

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

Explanation

f(n) (1) 56

(2) 28

(3) 14

(4) 7

To find the correct relation we have to test all of them.

A. f(n) = 28(0.5)^n

f(1) = 28(0.5)¹

      = 28 × 0.5 = 14  

f(n) = 28(0.5)^n ⇒  Not correct relation

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

    f(1) = 56(0.5)¹⁻¹  = 56×1

                              = 56

  F(2) = 56(0.5)²⁻¹  = 56 × 0.5  = 28

  F(3) = 56(0.5)³⁻¹  = 56 × 0.25 = 14

 f(n) = 56(0.5)^n-1  ⇒ It is the correct relation  

C. f(n) = 56(0.5)^n

   f(1) = 56(0.5)¹  = 56 × 0.5 = 28

f(n) = 56(0.5)^n  ⇒ Not correct relation

D. f(n) = 112(0.5)^n-1

  f(1) = 112(0.5)¹⁻¹  = 112 × 1 = 112

f(n) = 112(0.5)^n-1   ⇒ Not correct relation

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