Exercise 17 Page 351

The variable $P$ represents the atmospheric pressure in atmospheres at an altitude of $a$ meters. Since we want to find the pressure at $5000$ feet, first we convert feet to meters. Since $1$ foot is about $0.3048$ meters, $5000$ is about $5000\cdot 0.3048=1524$ meters. Next, we will find the atmospheric pressure at an altitude of $1524$ meters using a graphical calculator. First, we will draw $y=(0.99988{)}^x.$ To do this, push the button $\boxed{\text{Y=}}$ and enter the equation in the first row.

Having entered the function, we press the $\boxed{\text{GRAPH}}$ button to draw it on a coordinate plane. Also, we can change the scale of the $x\text{-}$axis to increase by $200.$ We can do this by pushing $\boxed{\text{WINDOW}}.$

To find the value of $(0.99988{)}^{1524},$ we can use the trace feature to find the value of the function at $x=1524.$ This can be done by pressing $\boxed{2\text{nd}},$ $\boxed{\text{TRACE}},$ and choosing the value option. Finally, enter $1524$ and it will give you the value of $(0.99988{)}^x$ when $x=1524.$

Rounded to three decimal places, the value of $(0.99988{)}^{1524}$ is around $0.833.$ Therefore, the atmospheric pressure at an altitude of $1524$ is around $0.833$ atmospheres.