To model spring fawn count F from adult pronghorn population A, precipitation P, and severity of the winter W, environmentalists have used the equation F = a + bA + cP + dW, where a, b, c, and d are constants that must be determined before using the equation. (Winter severity is scaled between 1 and 5, with 1 being mild and 5 being severe.)

Write an augmented matrix representing the system in Exercise 75, and solve for a, b, c, and d. Round coefficients to three decimal places.

Exercise 75

Substitute the values for F, A, P, and W from the table for Years 1–4 into the equation F = a + bA + cP + dW and obtain four linear equations involving a, b, c, and d.

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Year Fawns Adults Precip. (in inches) Winter Severity 239 871 11.5 3 2 234 847 12.2 192 685 10.6 5 4 343 969 14.2 1 960 12.6 3 3.