Chapter Test
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Decay factor: 0.99988
Decay rate: 0.00012=0.012 %
y= a(1- r)^t Here a is the initial amount, the decay factor is 1-r, and the decay rate is r. Next, consider the given function. P=( 0.99988)^a ⇓ P= 1* (1- 0.00012)^a Therefore, the initial amount is 1, the decay factor is 0.99988, and the decay rate is 0.00012.
Since 1 foot is about 0.3048 meters, 5000 is about 5000* 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 Y= and enter the equation in the first row.
Having entered the function, we press the GRAPH button to draw it on a coordinate plane. Also, we can change the scale of the x-axis to increase by 200. We can do this by pushing 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 2nd, 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.