The kilopascal is a unit of measure for atmospheric pressure. Suppose the atmospheric air pressure at sea level is about 96 kilopascals. For every​ 1000-m increase in​ altitude, the pressure decreases about 11.9​%. What is the approximate pressure at an altitude of 2000 ​m?

1.000 - .119 = 0.881

96 * (0.881)^n
where n is the number of 1000 meters we climb
Oh, look, that pesky geometric sequence again :)
96 * .881 * .881 = ?

Thank you

To find the approximate pressure at an altitude of 2000 m, we need to calculate the decrease in pressure based on the given percentage decrease and then subtract it from the initial pressure.

Step 1: Calculate the decrease in pressure for every 1000 m increase in altitude.
Decrease in pressure = 11.9% of 96 kPa
= (11.9/100) * 96 kPa
≈ 11.424 kPa

Step 2: Determine the number of 1000 m intervals in 2000 m.
Number of intervals = 2000 m / 1000 m
= 2 intervals

Step 3: Calculate the total decrease in pressure for 2000 m altitude.
Total decrease in pressure = Decrease in pressure per interval * Number of intervals
= 11.424 kPa * 2
≈ 22.848 kPa

Step 4: Subtract the total decrease in pressure from the initial pressure at sea level.
Pressure at 2000 m ≈ Pressure at sea level - Total decrease in pressure
≈ 96 kPa - 22.848 kPa
≈ 73.152 kPa

Therefore, the approximate pressure at an altitude of 2000 m is around 73.152 kilopascals.

To find the approximate pressure at an altitude of 2000 m, we can use the given information that the pressure decreases about 11.9% for every 1000 m increase in altitude.

1. Start with the original pressure at sea level: 96 kilopascals.
2. Determine the number of 1000 m increments for the given altitude of 2000 m. In this case, we have 2000 m / 1000 m = 2 increments.
3. For each increment of 1000 m, the pressure decreases about 11.9%. So, we need to calculate the decrease in pressure for 2 increments.
a. Calculate the decrease for one increment: 96 kilopascals * 11.9% = 11.424 kilopascals.
b. Calculate the decrease for two increments: 11.424 kilopascals * 2 = 22.848 kilopascals.
4. Subtract the total decrease from the original pressure to find the approximate pressure at the given altitude:
96 kilopascals - 22.848 kilopascals = 73.152 kilopascals.

Therefore, the approximate pressure at an altitude of 2000 m is approximately 73.152 kilopascals.