Exponential and logarithmic functions
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Drug Dosage
A drug prescription must be carefully planned to maximize benefit while avoiding an overdose. In this Gizmo, you can give a patient one … or more pills and monitor the levels of medication in the body through time. Based on the reaction of the patient, determine the ideal levels of medication. Create a dosage schedule so these levels are maintained through time. Four types of pills, each with a different release pattern and target organ, are available for use.
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Dye Elimination
When a foreign substance such as a drug is ingested, it often remains in the bloodstream for a long time. This Gizmo models the elimination … of substances from the bloodstream using water and dye. Add dye to a container of water, and then add beakers of pure water while removing beakers of dyed water. The amount of dye remaining is recorded after each cycle. The volumes of all containers can be adjusted, as well as the amount of dye used. This provides a good example of exponential decay.
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Exponential Functions - Activity A
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of … the function.
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Exponential Functions - Activity B
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of … the function.
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Exponential Functions - Activity C
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of … the function.
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Exponential Growth and Decay - Activity A
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate … the changes to the graph.
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Exponential Growth and Decay - Activity B
Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay. Investigate … the changes to the graph.
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Logarithmic Functions - Activity A
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes … in response. Use the line y = x to compare the associated exponential function.
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Logarithmic Functions - Activity B
Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes … in response. Use the line y = x to compare the associated exponential function.
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Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these … transformations with the domain of the function, and the asymptote in the graph.
