Solve the problem.
The function defined by P(x)=994e^0.0001308x approximates the atmospheric pressure (in millibars) at an altitude of x meters. Use P to predict the pressure at 0 meters and 10,000meters.
To predict the atmospheric pressure at 0 meters, we can substitute x = 0 into the equation P(x) = 994e^(0.0001308x):
P(0) = 994e^(0.0001308 * 0)
P(0) = 994e^0
P(0) = 994 * 1
P(0) = 994 millibars
Therefore, the predicted atmospheric pressure at 0 meters is 994 millibars.
To predict the atmospheric pressure at 10,000 meters, we can substitute x = 10,000 into the equation P(x) = 994e^(0.0001308x):
P(10,000) = 994e^(0.0001308 * 10,000)
P(10,000) = 994e^1.308
P(10,000) ≈ 994 * 3.698
P(10,000) ≈ 3,673.812 millibars
Therefore, the predicted atmospheric pressure at 10,000 meters is approximately 3,673.812 millibars.
To solve the problem, we need to use the formula provided:
P(x) = 994e^(0.0001308x)
To predict the pressure at 0 meters, we substitute x = 0 into the formula:
P(0) = 994e^(0.0001308*0)
= 994e^0
= 994 * 1
= 994 millibars
Therefore, the predicted pressure at 0 meters is 994 millibars.
To predict the pressure at 10,000 meters, we substitute x = 10,000 into the formula:
P(10,000) = 994e^(0.0001308*10,000)
Now, let's calculate it:
P(10,000) = 994e^(1.308)
= 994 * (approximately 3.6972) [using a calculator or software]
Therefore, the predicted pressure at 10,000 meters is approximately:
994 * 3.6972
= 3,670.6728 millibars.
So, the predicted pressure at 10,000 meters is approximately 3,670.6728 millibars.
To solve the problem, we will substitute the values of x into the function P(x) and calculate the predicted pressure at each altitude.
Step 1: Calculate the pressure at 0 meters:
Substitute x = 0 into the function P(x) = 994e^0.0001308x:
P(0) = 994e^0.0001308(0)
P(0) = 994e^0
P(0) = 994 * 1
P(0) = 994 millibars
Therefore, the predicted pressure at 0 meters is 994 millibars.
Step 2: Calculate the pressure at 10,000 meters:
Substitute x = 10,000 into the function P(x) = 994e^0.0001308x:
P(10,000) = 994e^0.0001308(10,000)
P(10,000) = 994e^1.308
P(10,000) ≈ 994 * 3.697
P(10,000) ≈ 3681.118
Therefore, the predicted pressure at 10,000 meters is approximately 3681.118 millibars.