Answer:
This is a problem in exponential decay.
a) If a town's population decreases by 4.5% every year that also means that the town's population decreases by a factor of .955 each year. (1 - .045 = .955)
So, after 5 years, the town's population is:
8,500 * .955^5 which equals 6,752.
So, basically, after t years, the town's population equals
8,500 * .955^t where t is the number of years that have passed since the year 2010.
b) population = 8,500 * .955 ^ (number of years since 2010)
7,000 / 8,500 = .955 ^ (number of years since 2010)
0.8235294118 = .955 ^ (number of years since 2010)
To solve for (number of years since 2010) we take logs of both sides
log (0.8235294118
) = number of years since 2010 * log(.955)
-0.0843208857 = number of years since 2010 * -0.0199966284
-0.0843208857 / -0.0199966284 = number of years since 2010
4.2167551422 = number of years since 2010
So, population = 7,000 when the year is 2014.2167551422
Or about 2.6 months into 2014
(YES, it's just that "easy") LOL
Step-by-step explanation:
