Exponential Decay And Effective Medicine Dosage
Now suppose that an additional dose of the drug is given to thepatient. Since we are assuming that when the drug is administered it is diffused so rapidly throughout the bloodstreamthat, for all practical purposes, it reaches its highest concentrationinstantaneously, we would see a jump in the concentration of the drugwhen the new dose is given, as shown in the graph below.
After the additional dose is given, the concentration again decays over time.
A problem facing physicians is the fact that for most drugs, there isa concentration, , below which the drug is ineffective and aconcentration, , above which the drug is dangerous. Thus thephysician would like the have the concentration satisfy
In the first part of this lab, we presentedthe expression
We can calculate theconcentration just before the second dose is administered by setting in our equation
This process can be continued and leads to the following two formulas. The first is the concentration just before the dose of the drug. This is
Now, suppose a treatment program is to be continued indefinitely. Theformulas above show that and . This means that the minimum concentration is theconcentration just before the second dose or
Benefits Of Sequence And Series Worksheets
The Sequence and Series Worksheets help the students on various aspects and topics, which are below-
- Provides an idea of finding the successive terms of a given sequence using explicit and recursive formulas.
- The worksheets put light on knowing about the general series and sequences of algebra.
- Students also develop ideas on evaluating the sequence and series of numbers, writing expressions on the geometric sequence, solving Arithmetic series, etc.
Transcription Of Geometic Sequences Geometric Sequences Multiplied
1 Algebra 2 GeometricSequences and series Notes Mrs. Grieser Name: _____ Date: _____ Block: _____ GeometicSequencesGeometricSequences contain a pattern where a fixed amount is multiplied from one term to the next after the first term Geometricsequence examples: o 2, 4, 16, 32, .. o Domain: _____ o Range: _____ o Graph shown at right o common ratio r = _____ o The graph of a Geometricsequence is _____ o Find the common ratio for the following GeometricSequences : a) 5, 10, 20, 40, .. r = _____ b) -11, 22, -44, 88, .. r = _____ c) 4, 38, 916, 2732, 8164, .. r = _____ Identifying GeometricSequences o Identify whether the following Sequences are arithmetic, Geometric , or neither.
2 If it is arithmetic, find d and if it is Geometric , find r. a) 4, 10, 18, 28, 40, .. _____ b) 625, 125, 25, 5, 1, .. _____ c) 81, 27, 9, 3, 1, .. _____ d) 1, 2, 6, 24, 120, .._____ e) -4, 8, -16, 32, -64, .._____ f) 8, 1, -6, -13, -20, .. _____ Algebra 2 GeometricSequences and series Notes Mrs. Grieser Page 2 Finding Terms in a Geometricsequence o Find the 7th term in the sequence : 2, 6, 18, 54, .. r = _____ a7 = _____ o Is there a pattern? a1 = 2 a2 = a1 r a3 = a2 r = a1 r r = _____ a4 = a3 r = a2 r r = a1 r r r = _____ an = _____ o You a) Find the common ratio r: 6, -3, 23, 43.
Recommended Reading: Holt Mcdougal Larson Geometry Workbook Answers
Sequences And Series Worksheets
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These Sequences and Series Worksheets are a good resource for students in the 8th Grade through the 12th Grade.
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Geometric Sequences And Series
A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
$$a_=a_\cdot r\ \: or\ \: a_=a_\cdot r^$$
Example
Write the first five terms of a geometric sequence in which a1=2 and r=3.
We use the first given formula:
$$a_=2$$
$$a_=2\cdot 3=6$$
$$a_=6\cdot 3=18$$
$$a_=18\cdot 3=54$$
$$a_=54\cdot 3=162$$
Just as with arithmetic series it is possible to find the sum of a geometric series. It is found by using one of the following formulas:
$$S_=\frac-a_\cdot r^}\ \ or\ \ S_=\frac}$$
Recommended Reading: Holt Geometry Practice Workbook Answer Key Pdf
Sequence And Series Worksheet
Sequence and Series Worksheet help the students to focus and solve the general sequencing problems and other topics related to Sequence and series. With the use of these worksheets, students can also have a good revision and practice the subject and topics that appear in the examination.
These sequences and series sheets will help students of CBSE higher secondary and senior secondary class students. The questions and the solutions of the worksheets are formulated as per the CBSE board and curriculum, along with the NCERT rules and guidelines.
The CBSE Board organizes the final term examinations to all the CBSE affiliated schools in India. Students should make proper preparation before appearing for the exam. The sequence and series worksheet help the students in scoring good marks in the final examination.