Question

Which is the graph of the sequence defined by the function f(x + 1) = 2/3 f(x) if the initial value of the sequence is 108?

Answer 1

1.

, then a=108,

2.

, then .

3. Check for x=2 and x=3:

a) x=2:

(true),

b) x=3:

(true).

4. Check for all x:

.

Equate f(x+1) and 2/3f(x):

is true equality for all x.

Answer: the graph is the graph of the function .