A coroner uses a formula, derived from Newton's Law of Cooling, to calculate the elapsed time

since a person died. The formula is

t = -10ln (T-R/ 37 - R) (note it is the whole T-R over the whole 37 -R)

where t is the time in hours since the death, T is the body's temperature measured inC and R

is the constant room temperature inC.

An accountant stayed late at work one evening and was found dead in his oce the next morning.

The office temperature was constant at 21C.

(a) At 10 am the coroner measured the body temperature. The temperature of the body was

found to be 29.7C. Determine the accountant's estimated time of death, leave your answer

correct to the nearest minute.

(b) What would the temperature of the body be at 10am, if the accountant had died at 2am?

(c) Sketch graphs of t versus T for R = 18, 21, 24 on the same axes, clearly showing the vertical

asymptote for each graph.