Question

problem 3 modeling exponential decay stem physics the kilopascal is a unit of measure for atmospheric pressure. the atmospheric pressure at sea - level is about 101 kilopascals. for every 1000 - m increase in altitude, the pressure decreases about 11.5%. what is the approximate pressure at an altitude of 3000 m?

Explanation:

Step1: Identify the decay - factor

The pressure decreases by 11.5% or 0.115 for every 1000 - m increase in altitude. So the decay - factor $r=1 - 0.115 = 0.885$.

Step2: Determine the number of 1000 - m intervals

The altitude is 3000 m. The number of 1000 - m intervals $n=\frac{3000}{1000}=3$.

Step3: Use the exponential - decay formula

The initial pressure $P_0 = 101$ kilopascals. The formula for exponential decay is $P = P_0\times r^n$. Substitute $P_0 = 101$, $r = 0.885$, and $n = 3$ into the formula: $P=101\times(0.885)^3$.

Step4: Calculate the result

$(0.885)^3=0.885\times0.885\times0.885\approx0.703$. Then $P = 101\times0.703\approx71$ kilopascals.

Answer:

71 kilopascals