Answer :
Final answer:
The patient's temperature reaches its maximum at about 12.1 hours into the illness, and this temperature is about 98.7 degrees Fahrenheit.
Explanation:
The temperature of the patient is modeled by a quadratic function T(t) = [tex]-0.012t^2 + 0.2904t + 98.1.[/tex] Quadratic functions achieve their maximum or minimum value (depending on the sign of the coefficient of the squared term) at their vertex.
The time at which the maximum occurs can be found by the formula t = -b/2a, where a is the coefficient of [tex]t^2[/tex], (a = -0.012), and b is the coefficient of t (b = 0.2904). Substituting these values, we find t = -0.2904 / 2*(-0.012) ≈ 12.1 hours.
The maximum temperature can be found by substituting t = 12.1 into the equation for T(t), which gives [tex]T(12.1) = -0.012(12.1)^2[/tex] + 0.2904*12.1 + 98.1 ≈ 98.7 degrees Fahrenheit.
Learn more about Quadratic functions here:
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