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

Relevance
  • Ash
    Lv 7
    4 weeks ago
    Favourite 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

Still have questions? Get answers by asking now.