SOLUTION: The population of a small town has been gradually decreasing over the past number of years. The equation: A = 1236(.97)t, where t is time in years, models the decrease in the town

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The population of a small town has been gradually decreasing over the past number of years. The equation: A = 1236(.97)t, where t is time in years, models the decrease in the town      Log On


   

Question 277893: The population of a small town has been gradually decreasing over the past number of years. The equation: A = 1236(.97)t, where t is time in years, models the decrease in the town’s population.
By what percent is the population decreasing yearly?
Answer: %
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Your formula should read:

A = 1236 * .97^T

The ^ sign indicates exponentiation.

The general formula for population increase or decrease is:

F = P * (1+G)^T where:

F = future population
P = present population
G = annual growth rate
T = number of years

Since your equation is shown as:

A = 1236 * .97^T, then:

F = A
P = 1236
1 + G = .97
T = number of years.

Since 1 + G = .97, this means that G = -.03 because 1 - .03 = .97

Your annual growth rate is -.03.

That's equivalent to -.03 * 100% = -3% which is a negative 3 percent per year.