Equivalent quadratic expressions
Immunization against the common cold
|
A research lab is trying to develop an immunization against the common cold.
Recent tests on a newly-developed substance have showed that taken in small doses it
reduces the chances of catching a cold. However, taken in large doses not only doesn't help but actually increases the chance of catching a cold.
During the study, different doses were given in the form of a pill to seven groups of people. Each group
consisted of several hundred people. Subjects were tracked for 4 months during the winter. A quadratic function describes the dependence on dosage (in miligrams) of the percentage of people that did not catch a cold.
|
| percentage of people who did not catch a cold |
|
|
dosage in miligarms
|
|
|
The following questions are important to researchers:
|
|
What are the chances (in percentages) of a person catching a cold during the winter without the immunization?
|
|
What is the recommended dosage for minimizing the chances of catching a cold?
|
|
Is there a dosage so large that it would cause a person to catch a cold for certain? If so, what is it?
|
|
At what dosage would the substance have no effect, so that the chances of
catching a cold would be the same as for those who were not immunized?
|
|
Use correspondence rules to present your answers
|
Construct a correpondence rule that describes the dependence of the chance of catching a cold on the dosage. Display a graph and a value table.
|
|
Answer the questions asked by the researchers. Explain how you can find the
answers using one or more of the function's representations (graph, value table, or correspondence rule).
|
|
Suggest other correspondence rules for the same function. Sugget a correspondence rule for each research question that enables you to glean the answer
to the question easily.
|
|
|
|
|
|
|
