Calc

posted by .

A body of an unknown temperature was placed in a room that was held at 30°F. After 10 minutes, the body's temperature was 0°F, and 20 minutes after the body was placed in the room the body's temperature was 15°F. Estimate the body's initial temperature.


Thank you!!

  • Calc -

    I am going to assume that the heat flow into the body is proportional to the difference between body temp T and 30 and rate of change of T is proportional to heat flow .

    dT/dt = k (30-T)

    try T = -ae^-kt + 30
    that is 30 at t-->oo and 30-a at t = 0
    so
    0 = -a e^-10k + 30
    15= -a e^-20k + 30

    30 = a e^-10k
    45 = a e^-20 k

    a = 30/e^-10k

    45 = 30 (e^-20k/e^-10k)

    45/30 = e^-10k

    I think you can take it from there, check arithmetic

  • Calc -

    the 8th line is the simplification of the sixth line,,, im wandering why it is 45? is the algebraic solution wrong?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Suppose that you are a CSI and you are called to a crime scene at 12:00 noon and find a dead body in a walk-in that is a constant 40¨H. The initial temperature is 85¡ã and after 20 minutes. The body¡¯s temperature is 84¡ã. Using …
  2. physics

    the temperature of a body falls from 30C to 20C in 5 minutes. The air temperature is 13C. Find the temperature after a further 5 minutes.
  3. math calculus

    In an experiment a persons body temperature is given by T=310-(7/9)^n where n is the number of minutes after in an experiment a persons body temperature is given by T=310-(7/9)^n where n is the number of minutes after the start of …
  4. math-urgent

    Newton’s Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium. The temperature u of a heated object at a given time t can be modeled by the …
  5. Newtons Law of Cooling

    using Newton's Law of Cooling: At 10:30 am the medical examiner arrives at a crime scene where a dead body has been found. The temperature of the body is 80 degrees F and the thermostat for the room in which the body was found is set …
  6. algebra

    A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 65°F. The temperature of the coffee after t minutes is given by T(t) = 65 + 115e^−0.042t.(a) Find the temperature, to the nearest degree, …
  7. Math

    A group of scientists found a new species of spider in the desert. The body temperature of the spider appears to vary sinusoidal over time. A maximum body temperature of the spider reaches 125?
  8. calculus

    Newton’s law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. So the rate of cooling for a bottle of lemonade at a room temperature of …
  9. Trigonometry URGENT!

    A group of scientists found a new species of spider in the desert. The body temperature of the spider appears to vary sinusoidal over time. A maximum body temperature of the spider reaches 125° after 15 minutes from the start of the …
  10. Maths

    The body of a murder victim was discovered at 11:00 A.M. and found the temperature of the body was 94.60°F. The temperature of the room was 700°F. One hour later, in the same room, he took the body temperature again and found it …

More Similar Questions