Atmospheric pressure changes as you rise above earth's surface. At an altitude of h kilometers, where 0<h<80, the pressure P is newtons per square centimeter is approximately modeled by the function P(h)=10.31e^(-0.116h). What is the approximate pressure at 50 kilometers. I have tried to figure this out and I keep getting the wrong answer. Please Help.
P(h) = 10.31e^(-0.116*50),
P(h) = 10.31*e^(-5.8),
P(h) = 10.31 * 0.003027554745=0.031214.
N/cm^2.
Seems low but I get the same answer every time.
To find the approximate pressure at 50 kilometers, we can substitute the value of h = 50 into the given function P(h) = 10.31e^(-0.116h). Let's calculate it step by step:
1. Start with the function: P(h) = 10.31e^(-0.116h).
2. Substitute h = 50 into the function: P(50) = 10.31e^(-0.116*50).
3. Simplify the exponent: P(50) = 10.31e^(-5.8).
4. Evaluate the exponential term (e^(-5.8)): P(50) ā 10.31 * 0.002576.
5. Calculate the final result: P(50) ā 0.0266 newtons per square centimeter.
Therefore, the approximate pressure at 50 kilometers is approximately 0.0266 newtons per square centimeter.