Question

At 1:00 a.m, a homocide detective found the reading of a corpse's body temperature to be 88 degrees Fahrenheit . One hour later, the body temperature is 83 degrees Fahrenheit. If the body has been in a 74 degrees Fahrenheit room since its death, what is the time of death assuming the body was at 98.6 degrees Fahrenheit at its death!

My answer: the equation is y=196/9(9/14)^x+74

When y=98.6
X is equal to -0.3
Is it -0.3 hour??
-0.3*60... How do you figure out the time?

Answer 1

I assume x is the number of hours since death (but y(0) = 95.7, which does not agree with the requirement that y(0) = 98.6)

Anyway, if you want to find the value of x for a given body temperature y using your equation,

y = 196/9 (9/14)^x + 74
(9/14)^x = 9/196 (y-74)
x = ln(9/196 (y-74))/ln(9/14)
= -0.4418 (ln(9/196) + ln(y-74))
= 1.3612 - 0.4418ln(y-74)

Fix the equation as needed and solve for x as above.