Question

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

Answer 1

answer is

f (x) = 108. (2/3)x

Answer 2

The correct graph is graph C

Explanation:

Given that a sequence defined by the function f(x + 1) =
`(2)/(3)` f(x)

Also given that initial value is 108

i.e. f(0) = 108

Applying the recurrence formula given we get

f(0+1) = 2/3 f(0) = 2/3 (108) = 72

Hence (1,72) should be next point

Now we have

f(2) = f(1+1) = 2/3 f(1) = 2/3 (72) =48

(2,48) is next point

f(3) = f(2+1) = 2/3 f(2) = 2/3 (48) = 32

(3,32) is the next point

The graph covering all these points is the graph C

Hence answer is graph C