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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Definitions:

Erik Erikson's Theory

A psychoanalytic theory of psychosocial development comprising eight stages from infancy to adulthood, each defined by a specific conflict.

Identity Versus Confusion

A stage in Erik Erikson's theory of psychosocial development where adolescents explore their independence and develop a sense of self.

Adolescence

The period of transition from childhood to adulthood, typically involving physical, psychological, and social changes.

Integrity Versus Despair

A stage in Erik Erikson's theory of psychosocial development in which aged individuals reflect on their life and either achieve a sense of satisfaction or fall into despair over unaccomplished goals.