Magic Bullets: Chemistry vs. Cancer

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    Cell Growth
    Doubling Up

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    Introduction
    Answers to Questions
    Cell Growth Chart
    Cell Growth Worksheet
    For more information, at other Web sites
    Relevant National Science Education Standards
    Relevant New Jersey State Science Education Standards

    Introduction

    This activity involves some math calculations. It also involves large numbers of invisible objects and so has application to many other areas of science as an exercise in managing large numbers. You may require your students to record all numbers in this exercise (or all greater than, say, 1000) in scientific notation.

    A table has been provided with enough room for 40 doubling times, in addition to the smaller table that appears in the activity.

    There are three things you might choose to emphasize in this activity:

    • Doubling time has broader application to other quantities. Consumption and production data may exhibit doubling time behavior or exponential behavior. Growth rates are sometimes exponential in nature. Doubling time is roughly related to rate in the following way:

      doubling time formula

    • Manipulation of large numbers

    • Effect of exposures early in life to cancer incidence later on

    A note on doubling: Without affecting outcomes too much, it is possible to round numbers off occasionally. For example, after 8 doubling times, there are 128 unit. After the next doubling period there would be 256. That, and other situations like it, may be rounded to 250 for ease of number management. Of course, the farther into the doubling times you go, the greater effect of rounding.

    Answers to Questions

    1. How many days have elapsed after 10 doubling times?

      1000 days

    2. Approximately how many years is this number of days?

      About 2 years, 9 months

    3. How many cells are present after 10 doubling times?

      512

    4. After 10 doubling times, would you be able to see the mass of cells?

      No

    5. How many doubling times would be required for the mass of cells to reach 1 mm?

      Somewhere in the 28th doubling period

    6. Approximately how many doubling times are required for 100 billion cells?

      About 38

    7. About how many years is that?

      About 10 years

    Cell Growth Chart

    Number of Doubling Times
    Number of Cells
    0

    1

    1

    2

    2

    4

    3

    8

    4

    16

    5

    32

    6

    64

    7

    128

    8

    256

    9

    512

    10

    1,024

    11

    2,048

    12

    4,096

    13

    8,192

    14

    16,384

    15

    32,768

    16

    65,536

    17

    131,072

    18

    262,144

    19

    524,288

    20

    1,048,576
    Number of Doubling Times
    Number of Cells
    21

    2,097,152

    22

    4,194,304

    23

    8,388,608

    24

    16,777,216

    25

    33,554,432

    26

    67,108,864

    27

    134,217,728

    28

    268,435,456

    29

    536,870,912

    30

    1,073,741,824

    31

    2,147,483,648

    32

    4,294,967,296

    33

    8,589,934,592

    34

    17,179,869,184

    35

    34,359,738,368

    36

    68,719,476,736

    37

    137,438,953,472

    38

    274,877,906,944

    39

    549,755,813,888

    40

    1,099,511,627,776

    Cell Growth Worksheet

    Two printable versions of the Cell Growth student worksheet are available for you to use. Click for either the Microsoft Word® version or the html version.

    For more information, at other Web sites...

      Cell Form and Function — a collection of activities and demonstrations from Biology - Resources for the Classroom, created by Jenni Gottschalk.

      Doubling Time — this interactive simulation calculates how fast a tumor will grow when you tell the computer how much it has grown since the last time you measured it, from ChestX-Ray.com. This site could be very useful in demonstrating cell-growth rates to students.

      Doubling Time and Population Growth — the math behind growth rates in human populations, from About.com.

      Growth Rate and Doubling Time — an in-depth look at the mathematics of growth rates of human, cell, and other populations, from the University of Toledo.

      The Population Bomb - Doubling Time — This exercise looks at the mathematics of human population increase (similar to that of cell reproduction) and the consequences of population growth, from KQED San Francisco and PBS Online.

      What Are Cells and Inside the Cell — learn the fundamental science of cells at these sites, from the National Institute of General Medical Sciences, National Institutes of Health.

    Relevant National Science Education Standards

      Unifying Concepts and Processes — This activity illustrates how cells change.

      Life Science — This activity also illustrates how cells change.

    Relevant New Jersey State Science Education Standards

      5.1 This activity requires students to draw conclusions from data.
      5.3 Math equations are required to understand doubling time and cell growth.
      5.5 The activity deals with cells and their growth.

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    Bibliography

      Respiration — part of the Web site Pulmonology from Universiteit Maastricht.

    Copyright ©2001 The Chemical Heritage Foundation