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

Answer: Fourth graph is the correct graph.

Explanation:

Since we have given that

Initial value of the sequence = f(x) = 108

And we have,

`f(x+1)=(2)/(3)f(x)`

So, Put x = 1, we have

`f(2)=(2)/(3)f(1)=(2)/(3)* 108=72\\\\f(3)=(2)/(3)f(2)=(2)/(3)* 72=48\\\\f(4)=(2)/(3)f(3)=(2)/(3)* 48=32`

So, its coordinates must be

(1,108), (2,72), (3,48), (4,32)

and it is satisfied by the graph (4).

Hence, Fourth graph is the correct graph.

Answer 2

The fourth graph.

Explanation:

We have f(x + 1) so the x values will be increased by 1.

first value = 108 (when x = 1)

next value = 108 * 2/3 = 72 (when x = 2)

next = 72 * 2/ 3= 48 (when x = 3)

next = 48 * 2/3 = 32 (when x = 4)