# Growth Decay question?

Equation: T = T0+(T1-T0)e^-kt

Normal body temp 37. Room temp 20.5, body temp 31.7.

50min later, body temp 28.1

What is the time of death to the nearest minute?

Please show me the steps...

Thank you

### 2 Answers

- AshLv 74 weeks agoFavourite answer
T = T₀+(T₁-T₀)e^(-kt)

31.7 = 20.5 + (37 - 20.5)e^(-kt)

31.7 = 20.5 + 16.5e^(-kt)

11.2 = 16.5e^(-kt)

e^(-kt) = 112/165 .............(1)

After 50 minutes

28.1 = 20.5 + (37 - 20.5)e^(-k(t+50))

7.6 = 16.5e^(-kt - 50k)

e^(-kt - 50k) = 7.6/16.5

e^(-kt)e^(-50k) = 76/165

from (1)

112/165 e^(-50k) = 76/165

e^(-50k) = (76/165)(165/112)

e^(-50k) = (19/28)

ln e^(-50k) = ln(19/28)

-50k = ln(19/28)

k = ln(19/28) / (-50)

k = 0.0078

plug in (1)

e^(-0.0078t) = 112/165

ln e^(-0.0078t) = ln(112/165)

-0.0078t = ln(112/165)

t = ln(112/165)/(-0.0078)

t = 50 min

The time of death is 50 min before the time at which body temperature was 31.7°C