Question

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

1) 28,000
2) 29,000
3) 30,000
4) 31,000

Answer 1

The estimated population of Bozeman, Montana, in the year 2005 is approximately 2) 29,000.

Step-by-step explanation:

To estimate the population of Bozeman in 2005, we can use the formula for exponential growth:

`\[ P(t) = P_0 * (1 + r)^t \]`

Where:

-
`\( P(t) \)` is the population at time
`\( t \)`,

-
`\( P_0 \)` is the initial population,

-
`\( r \)` is the growth rate,

-
`\( t \)` is the time in years.

Given that the initial population of Bozeman in 2000
`(\( P_0 \))` is 27,509, the growth rate
`(\( r \))` is 1.96% or 0.0196 (as a decimal), and the time
`(\( t \))` is 5 years (from 2000 to 2005), we can substitute these values into the formula:

`\[ P(5) = 27,509 * (1 + 0.0196)^5 \]`

Calculate the population:

`\[ P(5) \approx 27,509 * (1.0196)^5 \approx 28,988.86 \]`

Rounding to the nearest thousand, the estimated population of Bozeman in 2005 is approximately 29,000.

Therefore, the closest option is 2) 29,000.