Answer:
Step-by-step explanation:
Remarks
They want only the exponential equation, here's the point.
- You need to be dividing by a number barely over one.
- You need to reflect the idea that every 500 ft. the % is going to go down by approximately 1.8%. The model for an exponential result is not as good as a linear one (this is really better done a s a linear result, but I will be obedient to what is asked for).
- You ought to try so values just to see if the equation works.
Equation
[tex]\text{Amount the pressure becomes} = \dfrac{101 kpa}{(1+\dfrac{ 1.8}{100} )^\frac{h}{500} }[/tex]
What this gives you is the equation for a rise every 500 feet. To figure out the %
Use
[tex]\text {\% =} \frac{\text{101 - answer from above equation}}{101}*100\%[/tex]
Example
Let h = 1000 feet
101 / (1 + 1.8/100) ^ (1000/500)
101 / (1.018)^2
101 / 1.036324
97.46
Now take this number and use the second formula
% = (101 - 97.46)/101 * 100%
% = 3.54%
The answer should be 3.6% (2 * 1.8%)
This is close enough. The question does say approximately.
1500 feet will give you 5.2% which is close to 5.4 (1.8 * 3). The higher you go, the more it is going to be out, but the results will always be close.
