Calculus

posted by .

Time (min)0___10___20____30__40____50____60
Temp (F)68_72.64_76.97__80_82.9_85.38__87.5

Use the Trapezoidal Rule to find the best approximation you can for the average temperature in the trailer from 10:00 until 11:00.

(10/60)/2 (68 + 2(72.64) + 2(76.97) + 2(80) + 2(82.9) + 2(85.38) + 87.5)= 79.273

The temperature inside the trailer has been increasing since 10:00 AM at a rate proportional to the difference between it and the temperature outside the trailer (a cool 100 deg F). Write a differential equation and solve it. Use any of the items in the table to help you find the constants C and K.

dy/dt=k(100-y)
dy/(100-y)=kdt
-ln(100-y)=kt
100-y=e^-(kt)
100-y=Ce^-k (what do I do now and afterwards for the following questions?) Thanks for the help!

Use your diff-eq solution to find the average temp in the trailer between 10:00 and 11:00.

At 11:00 AM the temp outside was 100*F. Then it began to rise at a rate of 0.10 degrees per minute. I read somewhere that the cost of cooling a trailer accumulates at a rate of $0.005 per minute for each degree the outside temp exceeds 78*F. How much would you say it cost the school to keep you cool in that trailer from 11:15 until 11:45 AM?

  • Calculus -

    100-y=Ce^-k
    yes agree so y = 100 - C e^-kt
    let's call t = 0 at 10 am
    so at 10 am
    68 = 100 - Ce^0 = 100 -C
    so
    C = 32
    now
    y = 100 -32 e^-kt
    well, at t = 60 min which is 11 am, y = 87.5
    so
    87.5 = 100 - 32 e^-60 k
    32 e^-60 k = 12.5
    e^-60 k = .3906
    -60 k = ln .3906 = - .94
    k = .0157
    so in the end
    y = 100 - 32 e^-.0157 t

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus - Derivatives

    The approximation to a definite integral using n=10 is 2.346; the exact value is 4.0. If the approximation was found using each of the following rules, use the same rule to estimate the integral with n=30. A) Left Rule B) Trapezoid …
  2. Chemistry

    I don't understand this: For the temperature vs time graph for heat and changes of state. The graph starts at -2.1 degrees C The heat of fusion is at 2.0 degrees C The heat of vaporization is on 101.0 degrees C. The graph ends at 103.0 …
  3. calculus

    Use the trapezoidal rule and simpson's rule to approximate the value of the definite integral ∫2,1 ln xdx; n =4
  4. Physics

    Could someone please review my answers and tell me if I am on the right track?
  5. physical

    From t = 0 to t = 3.30 min, a man stands still, and from t = 3.30 min to t = 6.60 min, he walks briskly in a straight line at a constant speed of 1.76 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg …
  6. physical

    From t = 0 to t = 3.30 min, a man stands still, and from t = 3.30 min to t = 6.60 min, he walks briskly in a straight line at a constant speed of 1.76 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg …
  7. Calculus II - Trapezoidal Rule

    Find the error resulting from approximation by Trapezoidal Rule: integral (from 0 to 1) sqrt(1+ x^3) dx .... compute the results for n=8
  8. calculus

    Use the Trapezoidal Rule to approximate ¡Ò8 4 ln(x2+5) dx using n=3. Round your answer to the fourth decimal place.
  9. Calculus

    Use the trapezoidal rule with n = 5 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) from x=1 to 5
  10. PLEASE HELP BEEN STUCK ALL DAY CALCULUS

    Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral from 0 to 4 of x squared, dx.

More Similar Questions