BITACORA

First we started by guessing using this formula:

Ln / y - yt / = Kt + C



FIRST PART
On these part, we have to find if the crime was at the stated time, and we change the temperature from 0F to 0C, because is easier and we are used to work with these units.


Data:
Place temperature: 8:00 PM -- 300
y1 = 35.50 C t1= O ( 9:10 PM )
y2= 350C t2= 6 ( 9:16 PM )
y3= 37.50 C ( not sick person’s temperature) t3= X


First step:
We solve for C:

Ln/ 35.50 – 300 / = C

Because (K)(t) is equal to 0, so C is :
C = 1.7047

Second step:
We solve for K: (using the new value of C, and using the time difference of 6)

Ln/ 35.50 – 300 / = K (6) + 1.7047

1.6094 -1.7047 = 6K

K = - .015877

Third Step:
Now with the values of K and C and 37.50 as the initial temperature, we have to solve for the value of “t”, that would be the time.

Ln / 37.50 - 300 / = (-.015877) t + 1.7047

- 2.0149 – 1.7047 = t
.015877

t = 19.5378 min.




SECOND PART:
On this final part, we have to find again for the time with the same process used in the first part, but using new values of temperature, to confirm our investigations and find more possible answers.

Data:
Place temperature: 8:00 PM -- 300
y1 = 35.50 C t1= O ( 9:10 PM )
y2= 350C t2= 6 ( 9:16 PM )
y3= 37.50 C ( not sick person’s temperature) t3= X

Time—Temperature:

8:50 -- 30.80 C
9:00 -- 300C
9:10 -- 29.170C
9:16 -- 28.670C


First Step:
Solve for C:

Ln/ 35.50 -29.170/ = Kt + C

C=1.8453

Second Step:
Solve for K using value of C:

Ln/ 350C -29.170/= K(6) + 1..8453

1.84530 – 1.8453 = K
6
K= -.01371

Third Step:
Solve for the time using the values of C and K:

Ln/ 37.50C -29.170/= (-.01371 ) t + 1..8453

2.11986 – 1.8453 = t
.01371

t= 20.02 min

= 8:50 PM





Other temperatures, other possible answers:

with 37.80 = 22.60 min

with 370 15.50 min

with 380 24.27 min




Conclusion:

In our conclusion first we think that the problem obviously didnt have an exact answer, so we did different forms to solve and with the aproximations that we got. We can conclude that the murdered didn’t occur before the 8:50 because some approximations that we consider with the most appropriated temperature, showed us that the crime wasn’t committed before the 8:50.