The atmospheric pressure $p$ on a weather balloon decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the number of kilometers $\mathrm{h}$ above sea level by the function $p=710(2.7)^{-0.146 h}$. Complete parts a and $b$ below.
a. Find the atmospheric pressure at a height of 1 kilometer.
millimeters of mercury
(Round to the nearest tenth as needed)
Answer
Final Answer: The atmospheric pressure at a height of 1 kilometer is approximately \(\boxed{614.2}\) millimeters of mercury.
Step 1 ：Given the function \(p=710(2.7)^{-0.146 h}\), we need to find the atmospheric pressure at a height of 1 kilometer. This can be done by substituting \(h=1\) into the function.
Step 2 ：After substituting \(h=1\) into the function, we get \(p = 710(2.7)^{-0.146 \times 1}\).
Step 3 ：Calculating the above expression, we get \(p = 614.1567637883484\).
Step 4 ：Rounding to the nearest tenth, we get \(p = 614.2\).
Step 5 ：Final Answer: The atmospheric pressure at a height of 1 kilometer is approximately \(\boxed{614.2}\) millimeters of mercury.
