SOLUTION: The populations of Towns A, B, and C vary exponentially with respect to time. The population of Town A increases by 30% every 7 years. What is the annual percent change in the p

Algebra ->  Finance -> SOLUTION: The populations of Towns A, B, and C vary exponentially with respect to time. The population of Town A increases by 30% every 7 years. What is the annual percent change in the p      Log On


   

Question 1148897: The populations of Towns A, B, and C vary exponentially with respect to time.
The population of Town A increases by 30% every 7 years. What is the annual percent change in the population of Town A?
8.18826
Incorrect %
The population of Town B decreases by 38% every 15 years. What is the annual percent change in the population of Town B?
Incorrect %
The population of Town C triples every 11 years. What is the annual percent change in the population of Town C?
10.50315
Correct %

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The three problems are similar; if you can get the right answer for the last one, you must know the calculations that are needed. So you should be getting the right answers for the first two.

Town C....
The growth factor is 3 over 11 years:
x%5E11+=+3
x+=+3%5E%281%2F11%29+=+1.10503 to 5 decimal places
The growth factor for 1 year is 1.10503; that represents an increase of 10.503% per year. (your correct answer)

The calculations for the other cases are the same, with different numbers.

Town A....
The population increases by 30% in 7 years; that means a growth factor of 1+.30 = 1.30. So
x%5E7+=+1.3
and continue from there as before.

Town B....
The population decreases by 38% in 15 years; that means a "growth" factor of 1-.38 = 0.62. So
x%5E15+=+0.62
and again finish as with the other two cities.