Calc

Air pressure at sea level is 30 inches of mercury. At an altitude of h feet above the, air pressure, P, in inches of mercury, is given by,
P =30e^(-3.23x10-5h)
a)Find th equation of the tangent line at h=0.
b)A rule of thumb is given by travelers is that air pressure drops about 1 inch for every 1000-foot increase in height above sea level. Write a formula for the air pressure given by this rule of thumb.
Please HELP!!!!!

  1. 👍
  2. 👎
  3. 👁
  1. I don't know much about the physics of this topic, but when I sub in h=0 (sea level) I do not get 30 , like I should from the given equation.

    according to your rule of thumb
    we could have the following
    h P

    0 30
    1000 29 ---> two points (0,30) and (1000, 29)
    slope = (29-30)/(1000-0) = -1/1000

    P = (-1/1000)h + 30

    1. 👍
    2. 👎
  2. a) First: the definition of a tangent line is defined as a line passing through a given point of a function whose slope is equal to the derivative of the function at that point

    The equation of the tangent line is of the form y = mx + b, where m is the slope, and b is the y-intercept. Your function is not in terms of x and y, it is in terms of P and h, so the equation of the tangent line will look like P = m*h +b. This equation can be found after calculating the slope of P at h=0, and the value of P at h = 0

    The slope of P at h = 0 is equal to the derivative of P dP/dh evaluated at h = 0:

    dP/dh = (30*-3.23*10^-5)*e^(-3.23x10-5h)

    dP/dh(h=0) = (30*-3.23*10^-5) = -9.69*10^-4
    = m

    So far we have
    P = -9.69*10^-4 h + b

    we need to find b, the y intercept, to completely solve for the tangent line. We know that this point passes through P(h=0), or (0, 30)

    Put this point into the equation for the tangent line, and solve for b:

    30 = -9.69*10^-4*0 + b

    solve for b, b = 30;

    P = -9.69*10^-4*h + 30

    b) At h = 0, the air pressure is 30 inches of mercury. At 1000 feet, it would be 30 - 1000/1000 *1
    at 2000 feet, it would be
    30 - 2000/1000 * 1,

    so, examining the pattern:

    P = 30 - h/1000

    1. 👍
    2. 👎
  3. Thank you both for your help

    1. 👍
    2. 👎
  4. Jennifer, my point was that the equation, the way it was written, is not correct
    the exponent as typed was
    -3.23x10-5h
    When you sub in h=0, ----> -3.23x10 or -32.3

    The way you read it, what Andy probably meant to type is
    (-3.23 x 10^-5)h , but there is no exponent shown and following the order of operation yields the wrong result.

    We have been stressing the importance of the proper use of brackets to establish the correct order of operation.
    A agree with your tangent equation according to your interpretation , and noticed we also have the same linear equation.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    A scientist measures the boiling point of saltwater in a lab at an altitude of 800 feet above sea level. A second scientist measures the boiling point of freshwater in a lab at an altitude of 200 feet above sea level. When the

  2. engineering

    An aircraft flies at an altitude of 30,000 feet. Determine the air temperature (in [K]), air pressure (in [Pa]) and air density (in [kg/m3]) at this altitude, according to the standard atmosphere.

  3. Math

    The air temperature decreases by about 1 degree Fahrenheit for each 300 feet of altitude. a) Find a function T(x) for the temperature at an altitude of x feet if the sea-level temperature is 45∘F. (b) Find T(1000). [Round to two

  4. 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

  1. aeroneutical engineering

    An aircraft flies at an altitude of 30,000 feet. Determine the air temperature (in [K]), air pressure (in [Pa]) and air density (in [kg/m]) at this altitude, according to the standard atmospher

  2. calcq

    2- The earth’s atmospheric pressure p is often modeled by assuming that the rate dp/dh at Which p changes with the altitude h above sea level is proportional to p. Suppose that the pressure at sea level is 1013 millibars (about

  3. 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

  4. Chemistry

    You start at sea level on the beach in California. What would the atmospheric pressure be? Then you move to Los Angeles where the altitude is 87 meters above sea level what happens to the boiling point?

  1. Algebra 1

    Noa drove from the Dead Sea up to Jerusalem. When she arrived in Jerusalem after 1.5 hours of driving, her altitude was 710 meters above seal level. Her altitude increased at a constant rate of 740 meters per hour. Let y represent

  2. Science

    The air pressure on Pikes Peak in Colorado is approximately 600 millibars. What is the relationship between air pressure at the top of Pikes Peak and at sea level, where air pressure is 1013 millibars?

  3. math

    1. A submarine was suituated 800 feet below sea level. If it ascends 250 feet, what is it new position 2. Metal mercury at room temperature is a liquid. Its melting point is -39°C. The freezing point of alcohol is-114°C. How

  4. math

    atmospheric pressure decreases by about 12% for every 1000 meters you climb. The pressure at sea level is about 1.013 atmospheres. Construct a model to represent the atmospheric pressure at a given altitude in thousands of meters

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