Question

Which of the following includes the input-output pairs (2,4) and (3,8) ?

(A) The arithmetic sequence a₍ₙ₎ = 4n
(B) The linear function f(n)=2+4(n-1)
(C) The geometric sequence g₍ₙ₎ = 2⁽ⁿ⁻¹⁾)
(D) The exponential function h₍ₙ₎ = 2*2⁽ⁿ⁻¹⁾

Answer 1

The correct answer is Option D the exponential function h_n = 2*2^(n-1), which matches the input-output pairs (2,4) and (3,8).

Step-by-step explanation:

The student is asking which option (A) The arithmetic sequence an = 4n, (B) The linear function f(n)=2+4(n-1), (C) The geometric sequence gn = 2(n-1), or (D) The exponential function hn = 2*2(n-1) includes the input-output pairs (2,4) and (3,8). To find the correct answer, we need to plug the input values into each equation to see which one produces the corresponding output values.

Checking Option A:

a2 = 4(2) = 8 and a3 = 4(3) = 12, which does not match our pairs (2,4) and (3,8).

Checking Option B:

f(2) = 2+4(2-1) = 6 and f(3) = 2+4(3-1) = 10, which again does not match our pairs (2,4) and (3,8).

Checking Option C:

g2 = 2(2-1) = 2 and g3 = 2(3-1) = 4, which does not match our pairs (2,4) and (3,8).

Checking Option D:

h2 = 2*2(2-1) = 4 and h3 = 2*2(3-1) = 8, which matches our pairs (2,4) and (3,8).

Therefore, the correct answer is Option D, the exponential function hn = 2*2(n-1).