Find the exponential model for atmospheric pressure: P(x)=14.7(0.82)^x (sea level and 1 mile data)

Find the exponential function P(x)=a(b)^x that models atmospheric pressure (psi) given P(0)=14.7 and P(1)=12.054. Step-by-step solution showing a and b with exact decimals.

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We are given an exponential model of the form P(x)=a(b)x and two values:

  • P(0)=14.7
  • P(1)=12.054

Step 1: Use P(0) to find a. Since b0=1, a = P(0) = 14.7.

Step 2: Use P(1) to find b. P(1)=a·b = 14.7·b = 12.054, so

b = 12.054 / 14.7 = 0.82 (exact).

Therefore the model is:

P(x) = 14.7(0.82)x

Check: 14.7·0.82 = 12.054, which matches P(1).

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