Solve the problem.
The function defined by
P(x)=946e−0.0001277x approximates the atmospheric pressure (in millibars) at an altitude of x meters. Use P to predict the pressure at 0 meters and 15,000 meters.
To predict the pressure at 0 meters, we substitute x = 0 into the equation:
P(0) = 946e^(-0.0001277 * 0)
P(0) = 946e^0
P(0) = 946 * 1
P(0) = 946 millibars
Therefore, the predicted pressure at 0 meters is 946 millibars.
To predict the pressure at 15,000 meters, we substitute x = 15,000 into the equation:
P(15000) = 946e^(-0.0001277 * 15000)
P(15000) = 946e^(-1.9155)
P(15000) ≈ 175.34 millibars
Therefore, the predicted pressure at 15,000 meters is approximately 175.34 millibars.
To predict the atmospheric pressure at 0 meters and 15,000 meters using the function P(x) = 946e^(-0.0001277x), follow these steps:
Step 1: Substitute x = 0 into the function P
P(0) = 946e^(-0.0001277 * 0)
P(0) = 946e^(0)
P(0) = 946 * 1 (since e^0 = 1)
P(0) = 946 millibars
Therefore, the predicted atmospheric pressure at 0 meters is 946 millibars.
Step 2: Substitute x = 15000 into the function P
P(15000) = 946e^(-0.0001277 * 15000)
P(15000) ≈ 946e^(-1.9155)
You can use a calculator to approximate the value of e^(-1.9155).
P(15000) ≈ 946 * 0.1477 (approximate value of e^(-1.9155))
P(15000) ≈ 1395.9 millibars
Therefore, the predicted atmospheric pressure at 15,000 meters is approximately 1395.9 millibars.
To solve the problem, we need to evaluate the function P(x) for x = 0 and x = 15,000.
Given the function: P(x) = 946 * e^(-0.0001277x)
To find the pressure at 0 meters, we substitute x = 0 into the function:
P(0) = 946 * e^(-0.0001277 * 0)
= 946 * e^0
= 946 * 1
= 946 millibars
So, the predicted atmospheric pressure at 0 meters is 946 millibars.
To find the pressure at 15,000 meters, we substitute x = 15,000 into the function:
P(15000) = 946 * e^(-0.0001277 * 15000)
Calculating this using a calculator or a mathematical software:
P(15000) ≈ 946 * e^(-1.9155)
≈ 946 * 0.1474
≈ 139.39 millibars (approximately)
So, the predicted atmospheric pressure at 15,000 meters is approximately 139.39 millibars.