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A computer valued at $1500 loses 20% of its value each year.

a) write a function rule that models the value of the computer.

b) find he value of the computer after 3 years.

c) In how many years will the value of the computer be less then $500

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  1. 12 May, 15:27
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    A) The answer is F (n) = 1500 * 0.8ⁿ

    Let the function be F (n) where n is number of years

    After 20% is lost, the value that remains is 80% of 1500:

    1500 : 100%

    x : 80%

    1500 : 100% = x : 80%

    x = 1500 * 80% : 100%

    x = 1500 * 80/100

    x = 1500 * 0.8

    For each year we must add exponent, so the function is:

    F (n) = 1500 * 0.8ⁿ

    b) The answer is $768

    We have function: F (n) = 1500 * 0.8ⁿ

    And we know that the number of years is 3: n = 3

    F (3) = 1500 * 0.8³ = 1500 * 0.512 = 768

    c) The answer is 5 years

    We have function: F (n) = 1500 * 0.8ⁿ

    And we know that the value needs to be less then $500: F (n) = <500

    1500 * 0.8ⁿ < 500

    0.8ⁿ < 500 / 1500

    0.8ⁿ < 0.33

    log (0.8ⁿ) < log (0.33)

    n * log (0.8) < log (0.33)

    n * - 0.0969 < - 0.4815

    n < - 0.4815 / - 0.0969

    n < 5
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