Question

Which is the graph of the sequence defined by the function f(x + 1) = Two-thirdsf(x) if the initial value of the sequence is 108?

One a coordinate plane, 4 points are plotted. The points are (0, 108), (1, 36), (2, 12), (3, 4).

One a coordinate plane, 4 points are plotted. The points are (1, 108), (2, 36), (3, 12), (4, 4).

One a coordinate plane, 4 points are plotted. The points are (0, 108), (1, 72), (2, 48), (3, 32).

Answer 1

Use the recurrence f(x+1) = (2/3)f(x). Starting from 108 the terms are
f(0)=108,
f(1)=(2/3)·108=72,
f(2)=(2/3)·72=48,
f(3)=(2/3)·48=32.

So the points (0,108),(1,72),(2,48),(3,32) — the third graph.