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匿名 發問於 科學及數學數學 · 7 年前

F.3 Maths

1.The length of a neck-tie shrinks by 4% after each wash. If the original length of the neck-tie is 120cm, find the percentage change in the length of the neck-tie after 3 washes. (Give your answer correct to 1 decimal place.)

2. The price of a new device is $750. Its price increases at a rate of 5% per week for the first three weeks after issue, and then decreases at a rate of 9% per week for the following two weeks. Find the price of the device after 5 weeks of its issue. (GIVE YOUR ANSWER CORRECT TO THE NEAREST $1)

更新:

question 2, I do not know which step i did wrong, i always find out the answeris 720, the right answer is 719.

1 個解答

評分
  • 7 年前
    最愛解答

    smile, please also understand the method of the calculation rather than using our answers directly.

    1.

    After 3 washes, the length becomes 120*(1-4%)*(1-4%)*(1-4%) = 106.16832 cm

    The percentage change in length is

    (106.16832-120)/120*100% = -11.5264% = -11.5% (cor to 1 d.p.)

    2.

    The price of the device after 5 weeks is

    $750*(1+5%)*(1+5%)*(1+5%)*(1-9%)*(1-9%) = $718.971946875 = $719 (cor nearest $1)

    2013-07-25 18:05:35 補充:

    你說你計過幾次都係計到720,咁有可能係你唔係一次過計到尾,而係你分段咁計,而每步你都round左,有rounding error。

    例如:

    $750*(1+5%)=$787.5 round to $788

    $788*(1+5%)=$827.4 round to $827

    $827*(1+5%)=$868.35 round to $868

    $868*(1-9%)=$789.88 round to $790

    等等

    如果咁計,你有可能會累積d rounding error,要留意呢點。

    資料來源: Calculated
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