Question

Air pressure may be represented as a function of height (in meters) above the

Answer 1

Answer: OPTION C.

Step-by-step explanation:

The complete exercise is: "Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below:

 $P(h) =P_0e^{-0.00012h}$

In this function $P_o$   is the air pressure at the surface of the earth, and $h$ is the height above the surface of the Earth, measured in meters. At what height will the air pressure equal 50% of the air pressure at the surface of the Earth"

Given the following function:

$P(h) =P_0e^{-0.00012h}$

In order to calculate at what  height the air pressure will be equal 50% of the air pressure at the surface of the Earth, you can follow these steps:

1. You need to substitute $P(h)=0.5P_o$ into the function:

$0.5P_o=P_0e^{-0.00012h}$

2. Finally, you must solve for $h$.

Remember the following property of logarithms:

$ln(b)^a=a*ln(b)\\\\ln(e)=1$

Then, you get this result:

$0.5P_o=\frac{P_o}{e^{0.00012h}}\\\\(0.5P_o)(e^{0.00012h})=P_o\\\\e^{0.00012h}=\frac{P_o}{0.5P_o}\\\\ln(e)^{0.00012h}=ln(2)\\\\0.00012h*1=ln(2)\\\\h=\frac{ln(2)}{0.00012}\\\\h=5576.2$