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

First four terms of this sequence are:

.

This sequence is decreasing and seems to be exponential. See whether you can determine such a and b, that :

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.

the graph is the graph of the function .

See picture attached.

Step-by-step explanation:

For x = 1, f(x) = 108. For the next x-value which is 2, that is, x+1, f(x+1) = (2/3)*f(x) = (2/3)*108 = 72.   For the next x-value, which is 3, f(x+1) = (2/3)*f(x) = (2/3)*72 = 48 . For the next x-value, which is 4, f(x+1) = (2/3)*f(x) = (2/3)*48 = 32 . And so on.

xf(x)

1108

272

348

432

greater than one

step-by-step explanation: