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) = p₀e⁻⁰·⁰⁰⁰¹²ʰ
in this function, p₀ 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. 0.65 = h·e⁻⁰·⁰⁰⁰¹²
b. 0.65p₀ = p₀e⁻⁰·⁰⁰⁰¹²ʰ
c. h = 0.65e⁻⁰·⁰⁰⁰¹²
d. p₀ = 0.65p₀e⁻⁰·⁰⁰⁰¹²ʰ

Explanation:

Step1: Understand the problem

We know the air pressure function is \( P(h) = P_0 e^{-0.00012h} \), and we need to find the height \( h \) when the air pressure \( P(h) \) is 65% of \( P_0 \), that is \( P(h)=0.65P_0 \).

Step2: Substitute \( P(h) \)

Substitute \( P(h) = 0.65P_0 \) into the function \( P(h) = P_0 e^{-0.00012h} \). We get \( 0.65P_0=P_0 e^{-0.00012h} \).

Answer:

B. \( .65P_0 = P_0e^{-.00012h} \)