Question

The 2000 U.S. Census reports the populations of Bozeman, Montana, as 27,509 and Butte, Montana, as 32,370. 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×t^0.0196
Butte: P=32,370×t^0.9971

d. Bozeman: P=27,509×(0.0196)^t
Butte: P=32,370×(0.29)^t

Answer 1

The exponential functions that model the populations of Bozeman and Butte are: Bozeman: P=27,509×(1.0196)^t Butte: P =32,370×(0.9971)^t

Step-by-step explanation:

The exponential functions that model the populations of Bozeman and Butte can be determined using the given information from the 2000 U.S. Census. The correct choice is a. Bozeman: P=27,509×(1.0196)^t Butte: P =32,370×(0.9971)^t.

The exponential function for Bozeman is P = 27,509 × (1.0196)^t, where t represents the number of years since the census was conducted. This function represents growth, as the value of 1.0196 is greater than 1, indicating an increase in population over time.

The exponential function for Butte is P = 32,370 × (0.9971)^t. In this case, the value of 0.9971 is less than 1, indicating a decrease in population over time.