The atmospheric pressure P(h) (in pounds per square inch) at a height h (in miles) above sea level on Earth satisfies a differential equation P' = -kP for some positive constant k.

(a) Measurements with a barometer show that P(0) = 1.2 and P(9) = 0.7. What is the decay constant k?
(b) Determine the atmospheric pressure 14 miles above sea level.

  1. 👍
  2. 👎
  3. 👁
  1. P' = -kP
    dP/P = -k dh
    lnP = -kh + c

    P = c e^-kh
    P(0) = 1.2, so c = 1.2

    P = 1.2 e^-kh
    1.2 e^(-9k) = 0.7
    k = .06


    P(h) = 1.2 e^-.06h

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    The volume of a gas varies directly with its temperature and inversely with the pressure. If the volume of a certain gas is 20 cubic feet at a temperature of 350K and a pressure of 35 pounds per square inch, what is the volume of

  2. chemistry

    In which one of the following processes is ΔH = ΔE? a. 2HI(g) → H2(g) + I2(g) at atmospheric pressure. b. Two moles of ammonia gas are cooled from 325°C to 300°C at 1.2 atm. c. H2O(l) → H2O(g) at 100°C at atmospheric


    If the temperature is constant, then the atmospheric pressure P (in pounds/square inch) varies with the altitude above sea level h in accordance with the law given below where p0 is the atmospheric pressure at sea level and k is a


    According to Boyle's law, the pressure p of a compressed gas is inversely proportional to the volume, v. If a pressure of 20 pounds per square inch exists when the volume of the gas is 500 cubic inches, what is the pressure when

  1. Calculus

    The rate of change of atmospheric pressure P with respect to the altitude h is proportional to P provided that the temperature is consistent. At 15 degrees Celsius, the pressure is 101.3 pounds per square inch (psi) at sea level

  2. algebra

    when the temperature stays the same, the volume of the gas is inversely proportional to the pressure of the gas. If a balloon is filled with 87 cubic inches of a gas at a pressure of 14 pounds per square inch. Find the new


    PLEASE CHECK MY MATH ANSWERS PLEASE AND LABEL THEM LIKE 1.WRONG AND STUFF THANKS ! 1.There are 5 red crayons, 6 yellow crayons, and 11 blue crayons in a shoebox. What is the ratio of the total number of crayons to the number of

  4. science chemistry

    . O2 gas is slightly soluble in water. How does this affect the reported moles of KClO3 decomposed in the mixture? Explain. 2. a. When the water level inside the gas collecting test tube is higher than it is outside, is the O gas

  1. algebra

    The atmospheric pressure P in pounds per square inch (psi) is given by P = 14.7 e−0.21 a where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 12.31 psi, what is its altitude? (Recall that

  2. chemistry

    Which represents the largest pressure? A)five mmHg B)one atmosphere C)one millimeter of mercury D)one hundred pascals E)five pounds per square inch I tried converting them all to mmHg and I think the answer is B, but I just want

  3. precalculus

    The earth's atmospheric pressure, P, in terms of height above sea level is often modeled by an exponential decay function. The pressure at sea level is 1013 millibars and the pressure decreases by 14% for every kilometer above sea

  4. Help please? Chemistry

    At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure ____. I think it's supposed to be "contains the same number of molecules" but

You can view more similar questions or ask a new question.