Question

Air pressure may be represented as a function of height (in meters) above the
surface of the Earth, as shown below.
P(h) =P..e-0.00012h
In this function, P, is the air pressure at the surface of the Earth, and his 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?
A.4166.7m
B.2148.9m
C.5776.2m
D..59m

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:

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