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.

Question

anonymous · Answer

What are we trying to solve for? Finding the initial populations at 1990?

anonymous · Answer

exponential functions that model the populations of both cities

anonymous · Answer

Does it the date at which the models initial value should be based upon? Meaning should the initial value of the equation be at 1990 or 2000?

anonymous · Answer

2000

aum · Answer

y = a(1 + .0196)^x   for Bozeman, Montana
y = a(1 - .0029)^x    for Butte, Montana

I would base 1990 as the base year.
when x = 10, y = 27,509  for Bozeman, Montana.  Solve for a
when x = 10, y = 32,370  for Butte, Montana.  Solve for a

anonymous · Answer

Well all exponential equations are in the form y=a(b)^x 
a = the initial value
b = the growth rate

So if the models are based upon 2000 as the initial dates (meaning 2000 corresponds to x =0) then they have already given you all the information to answer the question. However if the models are based upon 1990 as the initial year, then you have to manipulate the equations to solve for a.

aum · Answer

"Since the 1990 census"  
tell me you should probably base it on 1990.

anonymous · Answer

so whats the answer?