SOLUTION: {{f Town B? C)The population of Town C triples every 6 years. What is the annual percent change in the population of Town C?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: {{f Town B? C)The population of Town C triples every 6 years. What is the annual percent change in the population of Town C?      Log On


   

Question 1129528: {{f Town B?
C)The population of Town C triples every 6 years. What is the annual percent change in the population of Town C?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
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he populations of Towns A, B, and C vary exponentially with respect to time.
The population of Town A increases by 19% every 13 years.
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y=ab%5Ex
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if a = 1,
y=1.19 after 13 years.
1.19=b%5E13

13%2Alog%28%28b%29%29=log%28%281.19%29%29

log%28%28b%29%29=0.005811

b=1.01347

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highlight_green%28y=a%281.01347%29%5Ex%29

To answer the first question, for each one unit change of x, there is increase by 1.35% in y.

Answer by greenestamps(13203) About Me  (Show Source):
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A) The population of town A increases by 19% every 13 years. If a is the starting population, the population after 13 years of growth will be 1.19a:

1.19a+=+ab%5E13
1.19+=+b%5E13
b+=+1.19%5E%281%2F13%29 = 1.01347 to 5 decimal places.

ANSWER: to 2 decimal places, the annual percent increase in population of town A is 1.35%.

B) The population of town B decreases by 40% every 14 years. If a is the starting population of town B, the population after 14 years will be 0.60a:

0.60a+=+ab%5E14
b+=+0.60%5E%281%2F14%29 = 0.96417 to 5 decimal places, which is 1-.03583.

ANSWER: to 2 decimal places, the annual change in the population of town B is -3.58%.

C) The population of town C triples every 6 years. If a is the starting population, the population after 6 years will be 3a:

3a+=+ab%5E6
b%5E6+=+3
b+=+3%5E%281%2F6%29 = 1.20093 to 5 decimal places.

ANSWER: to 2 decimal places, the annual percent change in the population of town C is 20.09%