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.

 Bozeman : , where x is number of years from 2000.

Butte: , where x is number of years from 2000.

Step-by-step explanation:

We know that the exponential growth function is given by :-

, where A is the initial value, r is the rate of increase and x is the time period.

Given: The population of Bozeman in 2000 = 27,509

The constant rate of increase = 1.96%=0.0196

Then, the exponential growth function that model the populations of Bozeman is given by :-

The population of Butte in 2000 = 32,370

The constant rate of decrease = 0.29% =0.0029

Then, the exponential growth function that model the populations of Butte is given by :-

one set of data has more variation than the other. hope this !

e^-kt = n/n0 = 0.79  

-kt = ln 0.79  

t = - ln 0.79/0.0001  

= 2357 years

step-by-step explanation: