SOLUTION: During an illness, a patient’s temperature (in C) is given by the function:
y = 37 + 0.9t - 0.075t2, where t is the number of days since the illness developed.
(a) Calcu
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y = 37 + 0.9t - 0.075t2, where t is the number of days since the illness developed.
(a) Calcu
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Question 1162490: During an illness, a patient’s temperature (in C) is given by the function:
y = 37 + 0.9t - 0.075t2, where t is the number of days since the illness developed.
(a) Calculate the maximum temperature during the illness, and when it occurred.
(b) When did the patient’s temperature return to normal (37 C)?
You can put this solution on YOUR website! Hi,
a) y = 37 + 0.9t - 0.075t^2
dy/dx = 0.9 - 0.075t
dy/dx = 0
0.9 - 0.075t = 0
- 0.075t = - 0.9
0.075t = 0.9 (Multiply both sides by -1)
t = 0.9/0.075
t = 12
Nature Table gives value t = 12 as a max.
b) By using the factorisation equation for the equation
t = -17 or t = 29
Therefore when temperature reaches 37 degrees = 29 days.
Hope this helps :-)
You can put this solution on YOUR website! During an illness, a patient’s temperature (in C) is given by the function:
y = 37 + 0.9t - 0.075t2, where t is the number of days since the illness developed.
(a) Calculate the maximum temperature during the illness, and when it occurred.
(b) When did the patient’s temperature return to normal (37 C)?
The other person who responded is WRONG!! a) Maximum temperature during illness occurs at the point where:
Maximum temperature during illness: b) Days that it took for temperature to return to :
t(0) = t(.9 - .075t)
0 = .9t - .75t OR 0 = t
0 = .9 - .075t
.075t = .9
Number of days that it took for temperature to return to , or
t = 0 (Day 0) signifies the INITIAL day at the beginning of the developmental stage
of the illness, when patient's INITIAL temperature was ALSO . FOOD FOR THOUGHT: WHY would someone use Calculus here? Does everyone know Calculus? I think NOT!!!
I place my post here to confirm the solution by the tutor @Math_Therapy.
It is about the maximum value of a quadratic function.
The quadratic function f(x) = ax^2 + bx + c of the general form with the negative leading coefficient a < 0
has the maximum value at x = .
In this case, a= -0.075, b= 0.9; therefore, the maximum temperature is achieved at
t = = = 6 days. ANSWER
The maximum temperature is equal to the value of the given function at t= 6 :
= = 39.7 °C. ANSWER
All questions are answered and the problem is solved.
