Question

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.

Answer 1

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.