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Atmospheric Pressure $\Leftrightarrow$ Atmospheric pressure $P$ (in kilopascals, $\mathrm{kPa}$ ) at altitude $h$ (in kilometers, $\mathrm{km}$ ) is governed by the formula$$\ln \left(\frac{P}{P_{0}}\right)=-\frac{h}{k}$$where $k=7$ and $P_{0}=100 \mathrm{kPa}$ are constants.a. Solve the equation for $P$.b. Use part (a) to find the pressure $P$ at an altitude of $4 \mathrm{km}$.

(a) $P=P_{0} e^{-h / k}$(b) $56.47 \mathrm{kPa}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 5

Exponential and Logarithmic Equations

McMaster University

Baylor University

University of Michigan - Ann Arbor

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at most Eric pressure is given by equation Allen Be overpay Nord equals minus Etch Viking. There, at 10-K I can't be known are constants. So we were KNP. Nor are constants and the value off case given to us at seven. On value off penal is 100 kilo Paschal No, in part a. We need to find our pressure. Atmospheric pressure. So equation four be that is atmospheric pressure at altitude edge, we will write Add a question here which is given to us Ln p l and b overpay nor equals minus vay cay Where at his altitude taking exponential both side bigger, bi, bi, bi nor equals it is to about minus at white gay. Now for the multiplying this equation throughout Bipin or Bigger beak will spin or in tow years to part minus X bike even substituted the value off B bean, R and K here, so bigger p equals 100 into eaters to pound minus at by seven. So this is that equation four at most. Eric pressure at altitude. It now for part B, we need to find the pressure at most. Eric pressure at on altitude off four kilometer. That is that is full. Now we will put the value at its port in equation number one and get at most Eric pressure. So P equals 100 in tow. Eaters to par minus pulled by seven. Since it is food now, calculating this, we get 100 in tow. We will use a calculator to solve this. So we get 0.56472 They're from a deep Langford that we get 56.472 Therefore, we have God that our atmospheric pressure like an altitude of four kilometers 56.472 kilo Pastor.

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