In my assignment, my Calculus teacher was murdered.

The three suspects are:

An English Teacher (no alibi from 9:15-10:00AM)

The Principal (no alibi from 10:05-10:50AM)

A History Teacher (no alibi from 10:55-11:40AM)

The temperature of the body was 87 degrees at 11:55AM, and 80 degrees at 12:45PM. The room was 75 degrees.

My job is to identify the murderer and support my answer with a written paragraph and some math.

I know I need to use (dy/dk)=K(y-Ts), e^(kt+c)=y-Ts, and y=Ce^(kt)+Ts

Assuming that Y = the temperature of an object, t = time, Ts = Room Temperature, and C = y - Ts. I have an example in my notes, but I am having trouble following the different equations and still get lost at the various transitions between e and ln.

Thank you in advance.