A Patient's Response to an Experimental Fever-Reducing Drug Can Be $D ( t ) = 0.025 t ^ { 2 } - 0.4 t$

question 147

Short Answer

A patient's response to an experimental fever-reducing drug can be modeled with the function $D ( t ) = 0.025 t ^ { 2 } - 0.4 t$ where t is the time in hours after taking a dose of the medication and D(t) represents the change in the patient's body temperature in Celsius degrees (see graph). a. What characteristics of D indicate that it is a quadratic function?
b. Find the times at which there is no fever reduction.
c. What points on the graph do the answers in part (b) represent?
d. At what times has the patient's temperature been reduced by 1.2°? [Hint: be sure to choose the correct sign for the temperature change. A reduction in temperature suggests what sign for the temperature change D(t)?]

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