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.