Labels of many food products have expiration dates, at which point they are typically removed from the supermarket shelves. A particular natural yogurt degrades (reacts) with a half-life of 45 days. The manufacturer of the yogurt wants unsold product pulled from the shelves when it degrades to no more than 80% (0.8) of its original quality. Assume the degradation process is first order. What should be the "best if used before" date on the container with respect to the date the yogurt was packaged?

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sampsonola sampsonola · Answer 1 · 2020-04-23T10:11:07+02:00

Answer:

Explanation:

Since it first order, we use order rate equation

In ( [tex]\frac{A1}{A0}[/tex]) = -kt where A1 is the final quality = 0.8 (80%), A0 is the initial quality = 1 ( 100%)

also, t half life = [tex]\frac{In2}{k}[/tex] where k is rate constant

k = [tex]\frac{In 2}{45 days}[/tex] = 0.0154

In ( [tex]\frac{0.8}{1}[/tex]) = - 0.0154 t

-0.223 / -0.0154 = t

t = 14.49 approx 14.5 days from the date the yogurt was packaged