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22 April, 18:37

The function f (x) = - 1/4 (x) + 1 is getting closer to a particular number. Its initial values are 4 and - 2, what happens to the values of the function's after 10 iterations. What number are the function's values getting closer to each time?

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  1. 22 April, 19:04
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    After 10 iterations, the value is approximately the value it gets closer each time, which is 0.8 (or 4/5)

    Step-by-step explanation:

    If the inicial value is 4, we have:

    1: f (4) = - 1/4 (4) + 1 = 0

    2: f (0) = - 1/4 (0) + 1 = 1

    3: f (1) = - 1/4 (1) + 1 = 3/4

    4: f (3/4) = - 1/4 (3/4) + 1 = 13/16

    5: f (13/16) = - 1/4 (13/16) + 1 = 51/64

    6: f (51/64) = - 1/4 (51/64) + 1 = 205/256

    7: f (205/256) = - 1/4 (205/256) + 1 = 819/1024

    8: f (819/1024) = - 1/4 (819/1024) + 1 = 3277/4096

    9: f (3277/4096) = - 1/4 (4) + 1 = 13107/16384

    10: f (13107/16384) = - 1/4 (13107/16384) + 1 = 52429/65536 = 0.8

    If the inicial value is - 2, we have:

    1: f (-2) = - 1/4 (-2) + 1 = 3/2

    2: f (3/2) = - 1/4 (3/2) + 1 = 5/8

    3: f (5/8) = - 1/4 (5/8) + 1 = 27/32

    4: f (27/32) = - 1/4 (27/32) + 1 = 101/128

    5: f (101/128) = - 1/4 (101/128) + 1 = 411/512

    6: f (411/512) = - 1/4 (411/512) + 1 = 1637/2048

    7: f (1637/2048) = - 1/4 (1637/2048) + 1 = 6555/8192

    8: f (6555/8192) = - 1/4 (6555/8192) + 1 = 26213/32768

    9: f (26213/32768) = - 1/4 (26213/32768) + 1 = 104859/131072

    10: f (104859/131072) = - 1/4 (104859/131072) + 1 = 419429/524288 = 0.8
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