Question

Pablo generates the function f (x) = three-halves (five-halves) Superscript x minus 1 to determine the xth number in a sequence.

Which is an equivalent representation?

f(x + 1) = Five-halvesf(x)
f(x) = Five-halvesf(x + 1)
f(x + 1) = Three-halvesf(x)
f(x) = Three-halvesf(x + 1)

Answer 1

The original function is f(x) = (3/2)*(5/2)^{x-1}. Compute

f(x+1) = (3/2)*(5/2)^{(x+1)-1} = (3/2)*(5/2)^x = (5/2)*[(3/2)*(5/2)^{x-1}] = (5/2) f(x).

So the equivalent representation is: f(x + 1) = Five-halves f(x).