Answer :
The maximum temperature is 102.2°F, and it occurs at 6.0 days. The correct answer is A. 102.2°F at 6.0 days.
To find the maximum value of the temperature and when it occurs, we need to find the vertex of the quadratic function T(t) = -[tex]0.1t^2 + 1.2t +[/tex]98.6.
The vertex of a quadratic function is given by the formula:
t = -b / (2a)
In our case, a = -0.1 and b = 1.2.
t = -1.2 / (2 * (-0.1))
t = -1.2 / (-0.2)
t = 6
So, the maximum temperature occurs at t = 6 days.
To find the maximum temperature, we substitute t = 6 into the function T(t):
[tex]T(6) = -0.1(6)^2 + 1.2(6) + 98.6[/tex]
T(6) = -0.1(36) + 7.2 + 98.6
T(6) = -3.6 + 7.2 + 98.6
T(6) = 102.2
Therefore, the maximum temperature is 102.2°F, and it occurs at 6.0 days.
The correct answer is A. 102.2°F at 6.0 days.
Learn more about quadratic function here:
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Assume that the temperature T of a person during a certain illness is given by T(t)=−0.1t^2 +1.2t+98.6,0≤t≤12 where T= the temperature ( ∘ F) at time t, in days. Find the maximum value of temperature and when it occurs. Round to one decimal place. A. 102.2 ∘ F at 6.0 days B. 100.9 ∘ F at 4.8 days C. 102.2 ∘ F at 3.6 days D. 101.2 ∘ F at 6.0 days
