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28 April, 21:44

Liam is making barbecue ribs over a fire. The internal temperature of the ribs when he starts cooking is 40°F. During each hour of cooking, the internal temperature will increase by 25%. The ribs are safe to eat when they reach 165°F.

Use the drop-down menus to complete an inequality that can be solved to find how much time, t, it will take for the internal temperature to reach at least 165°F.

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  1. 28 April, 22:06
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    Answer: You need to wait at least 6.4 hours to eat the ribs.

    t ≥ 6.4 hours.

    Step-by-step explanation:

    The initial temperature is 40°F, and it increases by 25% each hour.

    This means that during hour 0 the temperature is 40° F

    after the first hour, at h = 1h we have an increase of 25%, this means that the new temperature is:

    T = 40° F + 0.25*40° F = 1.25*40° F

    after another hour we have another increase of 25%, the temperature now is:

    T = (1.25*40° F) + 0.25 * (1.25*40° F) = (40° F) * (1.25) ^2

    Now, we can model the temperature at the hour h as:

    T (h) = (40°f) * 1.25^h

    now we want to find the number of hours needed to get the temperature equal to 165°F. which is the minimum temperature that the ribs need to reach in order to be safe to eaten.

    So we have:

    (40°f) * 1.25^h = 165° F

    1.25^h = 165/40 = 4.125

    h = ln (4.125) / ln (1.25) = 6.4 hours.

    then the inequality is:

    t ≥ 6.4 hours.
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