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The 2000 u. S. Census reports the populations of bozeman, montana, as 27,509 and butte, montana, as 32,370. Since the 1990 census, bozeman’s population has been increasing at approximately 1.96% per year. Butte’s population has been decreasing at approximately 0.29% per year. Assume that the growth and decay rates stay constant. Determine the exponential functions that model the populations of both cities.
a. Bozeman: P=27,509⋅(1.0196)ᵗ Butte: P=32,370⋅(0.9971)ᵗ
b. Bozeman: P=32,370⋅(1.0196)ᵗ Butte: P=27,509⋅(0.9971)ᵗ
c. Bozeman: P=27,509⋅(0.0196)ᵗ Butte: P=32,370⋅t0.9971
d. Bozeman: P=27,509⋅(0.0196)ᵗ Butte: P=32,370⋅(0.9971)ᵗ

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