Solve the problem.
The function defined by
P(x)=1007e−0.0001272x approximates the atmospheric pressure (in millibars) at an altitude of x meters. Use P to predict the pressure at 0 meters and 13,000 meters.
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Question content area right
Part 1
The pressure at 0 meters is
10071007 millibars.
Part 2
The pressure at 13,000 meters is
enter your response here millibars.
(Round to the nearest whole number.)
To find the pressure at 0 meters, we need to plug in x = 0 into the equation P(x) = 1007e^(-0.0001272x):
P(0) = 1007e^(-0.0001272(0))
P(0) = 1007e^(0)
P(0) = 1007 * 1
P(0) = 1007 millibars
Therefore, the pressure at 0 meters is 1007 millibars.
To find the pressure at 13,000 meters, we need to plug in x = 13,000 into the equation P(x) = 1007e^(-0.0001272x):
P(13,000) = 1007e^(-0.0001272(13,000))
P(13,000) = 1007e^(-1.6516)
P(13,000) ≈ 1007 * 0.1912
P(13,000) ≈ 192.9
Rounded to the nearest whole number, the pressure at 13,000 meters is 193 millibars.
To solve the problem, we'll substitute the given values into the function P(x)=1007e^(-0.0001272x).
Part 1: The pressure at 0 meters can be found by substituting x = 0 into the function.
P(0) = 1007e^(-0.0001272 * 0)
P(0) = 1007e^0
P(0) = 1007 * 1
P(0) = 1007 millibars
Therefore, the pressure at 0 meters is 1007 millibars.
Part 2: The pressure at 13,000 meters can be found by substituting x = 13,000 into the function.
P(13000) = 1007e^(-0.0001272 * 13000)
P(13000) = 1007e^(-1.6516)
Using a calculator, we can find that e^(-1.6516) is approximately 0.1911 (rounded to four decimal places).
P(13000) ≈ 1007 * 0.1911
P(13000) ≈ 192.3377
Rounding to the nearest whole number, the pressure at 13,000 meters is approximately 192 millibars.
Therefore, the pressure at 0 meters is 1007 millibars, and the pressure at 13,000 meters is approximately 192 millibars.
To solve this problem, we are given the function P(x) = 1007e^(-0.0001272x), which represents the atmospheric pressure in millibars at an altitude of x meters.
To find the pressure at 0 meters, we need to substitute x = 0 into the function:
P(0) = 1007e^(-0.0001272 * 0)
= 1007e^0
= 1007 * 1
= 1007 millibars.
Therefore, the pressure at 0 meters is 1007 millibars.
To find the pressure at 13,000 meters, we need to substitute x = 13,000 into the function:
P(13,000) = 1007e^(-0.0001272 * 13,000)
Calculating this value may require a calculator or software. After evaluating the expression, we find that P(13,000) ≈ 363.453 millibars.
Rounding this value to the nearest whole number, we get the final answer:
The pressure at 13,000 meters is approximately 363 millibars.