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:

The fourth graph.

Step-by-step 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)

Answer 2

Answer: Fourth graph is the correct graph.

Step-by-step explanation:

Since we have given that

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

And we have,

$f(x+1)=\frac{2}{3}f(x)$

So, Put x = 1, we have

$f(2)=\frac{2}{3}f(1)=\frac{2}{3}\times 108=72\\\\f(3)=\frac{2}{3}f(2)=\frac{2}{3}\times 72=48\\\\f(4)=\frac{2}{3}f(3)=\frac{2}{3}\times 48=32$

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.