## 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 **Geometric****Sequences** and **series** Notes Mrs. Grieser Name: _____ Date: _____ Block: _____ **Geometic****Sequences****Geometric****Sequences** contain a pattern where a fixed amount is **multiplied** from one term to the next after the first term **Geometric****sequence** examples: o 2, 4, 16, 32, .. o Domain: _____ o Range: _____ o Graph shown at right o common ratio r = _____ o The graph of a **Geometric****sequence** is _____ o Find the common ratio for the following **Geometric****Sequences** : a) 5, 10, 20, 40, .. r = _____ b) -11, 22, -44, 88, .. r = _____ c) 4, 38, 916, 2732, 8164, .. r = _____ Identifying **Geometric****Sequences** 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 **Geometric****Sequences** and **series** Notes Mrs. Grieser Page 2 Finding Terms in a **Geometric****sequence** 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

Here is a graphic preview for all of the **Sequences and Series Worksheets**. You can select different variables to customize these Sequences and Series Worksheets for your needs. The Sequences and Series Worksheets are randomly created and will never repeat so you have an endless supply of quality Sequences and Series Worksheets to use in the classroom or at home. We have general sequences, arithmetic sequences, geometric sequences, comparing arithmetic and geometric sequences, general series, arithmetic series, arithmetic and geometric means with sequences, finite geometric series, and infinite geometric series for your use.Our Sequences and Series Worksheets are free to download, easy to use, and very flexible.

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.