Question

a meteorologist uses the function $p(x)=29.9(0.89)^x$ to model the atmospheric pressure, in inches of mercury, at an altitude of $x$ kilometers above sea level. according to the model, how does the atmospheric pressure change with altitude? the atmospheric pressure increases by 11% per kilometer. the atmospheric pressure decreases by 89% per kilometer. the atmospheric pressure decreases by 11% per kilometer. the atmospheric pressure increases by 89% per kilometer.

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay function is $y = a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay, and $x$ is the number of time - intervals. In the given function $P(x)=29.9(0.89)^x$, we can rewrite $0.89$ as $1 - 0.11$.

Step2: Identify the rate of change

Comparing $P(x)=29.9(0.89)^x$ with $y = a(1 - r)^x$, we have $1 - r=0.89$, so $r = 0.11$ or $11\%$. Since it is in the form of an exponential - decay function, the atmospheric pressure decreases as $x$ (altitude) increases.

Answer:

The atmospheric pressure decreases by 11% per kilometer.