A bag contains 63 marbles, some white and some green. The ratio of white marbles to green ones is 2:7.
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Answer:
<em>12 hours </em>are required to be less than 10 milligrams of caffeine in Faye's body
Step-by-step explanation:
<u>Geometric sequences </u>
We can recognize a geometric progression, when we can get each member n as the previous member n-1 multiplied or divided by a constant value, called the common ratio.
Faye holds 120 milligrams of caffeine. We know each hour the amount of caffeine in her body will be 80% of the amount from the previous hour. For example, the first hour she will hold 80%(120)=96 milligrams of caffeine. Next hour it will be 80%(96)=76.8 and so on
We can see the sequence of contents of caffeine follows the rule of a geometric sequence and the common ratio is 80%, i.e. 0.8. The first term is 120, so the general term of the sequence is
We are required to find how much time is needed to be less than 10 milligrams of caffeine remaining in Faye's body. It can be stated that
Let's solve for t. Operating
Taking logarithms in both sides
Applying the power property of logarithms
Solving for t. Since ln0.8 is negative, the direction of the inequality changes
Rounding to the next integer
12 hours are required to be less than 10 milligrams of caffeine in Faye's body