Find the exponential atmospheric pressure model P(x)=a(b)^x given P(0)=14.7 and P(1)=12.054

Step-by-step solution to find the exponential model for atmospheric pressure: determine a and b from P(0)=14.7 and P(1)=12.054 and write P(x)=14.7(0.82)^x.

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We are given P(x)=a(b)^x and two values:

  1. At x=0: P(0)=a(b)^0=a=14.7, so a=14.7.
  2. At x=1: P(1)=14.7·b=12.054, so b=12.054/14.7 = 0.82.

Therefore the model is:

P(x)=14.7(0.82)^x

(You can check: P(1)=14.7·0.82=12.054.)

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