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)?
<pre>The other person who responded is <b><font color="red">WRONG!!</font></b>
{{{matrix(1,3, y, "=", 37 + .9t - .075t^2)}}}
<b>a)</b>	Maximum temperature during illness occurs at the point where: {{{highlight_green(matrix(1,9, "t(time)", "=", (- b)/(2a), "=", (- .9)/(2 * - .075), "=", (- .9)/(- .15), "=", highlight(matrix(1,2, 6, days))))}}}
        Maximum temperature during illness: {{{highlight_green(matrix(1,5, f(6), "=", 37 + .9(6) - .075(6)^2, "=", highlight(matrix(1,2, 39.7^o, C))))}}}
<b>b)</b>	Days that it took for temperature to return to {{{matrix(1,2, 37^o, C)}}}: {{{matrix(3,3, y, "=", 37 + .9t - .075t^2, 
37, "=", 37 + .9t - .075t^2 ,
0, "=", .9t - .075t^2)}}}
                                                                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 {{{matrix(1,2, 37^o, C)}}}, or {{{highlight_green(matrix(1,5, t, "=", .9/.075, "=", highlight(12)))}}}
                                                                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 {{{matrix(1,2, 37^o, C)}}}.
<b>FOOD FOR THOUGHT:</b> WHY would someone use Calculus here? Does everyone know Calculus? I think NOT!!!