Question

A meteorologist is monitoring the atmospheric pressure as his height above sea level varies. The meteorologist determines that the atmospheric pressure decreases by 12% for each additional kilometer the city is above sea level. The atmospheric pressure at sea level is 103 kPa (kilopascals).
a. Define a function, p, that determines the atmospheric pressure (in kPA) in terms of the number of kilometers the city is above sea level, n.

b. If the atmospheric pressure is 72 kPa what is your elevation above sea level (in kilometers)?

c. If the atmospheric pressure is 98 kPa what is your elevation above sea level (in kilometers)?

d. What is the atmospheric pressure, in kPa, when you are 20 kilometers above sea level?

Answer 1

(a)
$p(n)=103(0.88)^{n}$

(b)
$72=103(0.88)^{n}$
$\frac{72}{103}=0.88^{n}$
Taking logs of both sides, we get:
$log(\frac{72}{103})=n\ log\ 0.88$
$n=\frac{log\frac{72}{103}}{log0.88}=2.8\ km$

(c)
$n=\frac{log\frac{98}{103}}{log0.88}=0.389\ km\ or\ 389\ m$

(d)
$p=103(0.88)^{20}=8\ kPa$