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Gemiola [76]
3 years ago
7

What is the explicite to 19,13,7,1,...

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0
19, 13,  7,  1,…
  - 6  - 6  - 6

Something that is explicit to the problem is tat it has a common difference of -6.

a(n) = a₁ + d(n - 1)
a(n) = 19 - 6(n - 1)
a(n) = 19 - 6(n) + 6(1)
a(n) = -6n + 19 + 6
a(n) = -6n + 25
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3 years ago
A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%
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Answer:

a. A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\

b. \frac{dA}{dt}= -11.25 \frac{mg}{h}

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

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The rate is negative as it represents the amount of caffeine leaving the body at certain time.

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3 years ago
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