Identify the initial amount, decay factor, and decay rate.
Understand the Problem
The question is asking to identify specific parameters from the given mathematical model of atmospheric pressure. These parameters include the initial amount, the decay factor, and the decay rate based on the provided formula.
Answer
Initial Amount: 1 atmosphere, Decay Factor: 0.99988, Decay Rate: 0.00012
Answer for screen readers
- Initial Amount: 1 atmosphere
- Decay Factor: 0.99988
- Decay Rate: 0.00012
Steps to Solve
- Identify the Initial Amount
The equation given is $P = (0.99988)^a$. In this exponential model, the initial amount represents the pressure at an altitude of 0 meters, which is calculated by setting $a = 0$:
$$ P(0) = (0.99988)^0 = 1 $$
Thus, the initial amount is 1 atmosphere.
- Determine the Decay Factor
The decay factor in an exponential model is the base of the exponent. Here, the decay factor is:
$$ \text{Decay Factor} = 0.99988 $$
- Calculate the Decay Rate
The decay rate can be found using the formula for decay rate which is calculated as $1 - \text{Decay Factor}$. Therefore:
$$ \text{Decay Rate} = 1 - 0.99988 = 0.00012 $$
- Initial Amount: 1 atmosphere
- Decay Factor: 0.99988
- Decay Rate: 0.00012
More Information
The initial amount indicates that at sea level (0 meters), atmospheric pressure is 1 atmosphere. The decay factor suggests that as altitude increases, atmospheric pressure decreases slightly; the decay rate quantifies this decrease per unit of altitude.
Tips
- Confusing the initial amount with the decay factor.
- Not properly calculating the decay rate by neglecting to subtract the decay factor from 1.
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