A meteorologist measures the atmospheric pressure P (in kilograms per square meter) at altitude h (in kilometers). The data are shown below. Find the rate of change of the pressure with respect to altitude when using the relation . Round your answer to one decimal place.

Question

A meteorologist measures the atmospheric pressure P (in kilograms per square meter) at altitude h (in kilometers). The data are shown below. Find the rate of change of the pressure with respect to altitude when  using the relation  . Round your answer to one decimal place.

Quizplus · Accepted Answer

We are given that P=95e^(-0.12h) and asked to find dP/dh when h=11. To find the derivative, we will need to use the chain rule:

dP/dh = dP/d(e^(-0.12h)) * d(e^(-0.12h))/dh

We can find the first derivative as:

dP/d(e^(-0.12h)) = -0.12 * 95e^(-0.12h) = -11.4e^(-0.12h)

And the second derivative as:

d(e^(-0.12h))/dh = -0.12e^(-0.12h)

Putting it all together:

dP/dh = -11.4e^(-0.12h) * -0.12e^(-0.12h)

At h=11, this becomes:

dP/dh = -11.4e^(-1.32) * -0.12e^(-1.32)

dP/dh ≈ 0.8

Rounding to one decimal place, we get the final answer of 0.8, which corresponds to choice B.

A Meteorologist Measures the Atmospheric Pressure P (In Kilograms Per