The graph of the sequence defined by the function f(x + 1) = (2/3)f(x) and initial value of the sequence given is 108 is on a coordinate plane, 4 points are plotted; the points are (0, 108), (1, 72), (2, 48), (3, 32). This can be obtained by taking f(0) as 108 since it is the initial value and substituting in the function to get other values.
Which is the required graph?
Given the function, f(x + 1) = (2/3)f(x) and initial value f(0)=108
Therefore the first point is (0,108)
- Substitute in the function,
f(0 + 1) = (2/3)f(0) ⇒ f(1) = (2/3)108 = 72
∴the second point is (1,72)
- Again substitute in the function,
f(1 + 1) = (2/3)f(1) ⇒ f(2) = (2/3)72 = 48
∴the third point is (2,48)
- Similarly substitute in the function,
f(2 + 1) = (2/3)f(2) ⇒ f(3) = (2/3)48 = 32
∴the fourth point is (3,32)
Hence the graph of the sequence defined by the function f(x + 1) = (2/3)f(x) and initial value of the sequence given is 108 is on a coordinate plane, 4 points are plotted; the points are (0, 108), (1, 72), (2, 48), (3, 32). Therefore the correct answer is option 3.
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