Two towns had a population of 12,000 in 1990. by 2000, the population of town a had increased by 8 ⁢ % while the population of town b had decreased by 8 ⁢ %. assume these growth and decay rates continued.

For this problem what we should do is write an exponential function for each town.

We can write the exponential function for decades:

town a =

p (t) = 12000 (1.08) ^ (t)

town b =

p (t) = 12000 (0.92) ^ (t)

In both cases:

t = number of decades.

We can write the exponential function for years:

town a =

p (t) = 12000 (1.08) ^ ((1/10) * t)

town b =

p (t) = 12000 (0.92) ^ ((1/10) * t)

In both cases:

t = number of years.