Question

question 1 of 10
air pressure may be represented as a function of height above the surface of the earth as shown below.
$p(h)=p_{o}e^{-.0012h}$
in this function, $p_{0}$ is air pressure at sea - level, and $h$ is measured in meters.
which of the following equations will find the height at which air pressure is 65% of the air pressure at sea - level?
a. $.65 = hcdot e^{-.0012}$
b. $.65p_{o}=p_{o}e^{-.0012h}$
c. $p_{o}=.65p_{o}e^{-.0012h}$
d. $h =.65e^{-.0012}$

Explanation:

Step1: Set up the air - pressure condition

We know that the air pressure function is $P(h)=P_0e^{-0.0012h}$, and we want to find the height $h$ when the air pressure $P(h)$ is 65% of the air pressure at sea - level $P_0$. So $P(h) = 0.65P_0$.

Step2: Substitute into the function

Substitute $P(h)=0.65P_0$ into the function $P(h)=P_0e^{-0.0012h}$, we get $0.65P_0=P_0e^{-0.0012h}$.

Answer:

B. $.65P_0 = P_0e^{-.0012h}$