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# The population of the Midwest industrial town decreased from 224,000 to 219,000 in just 2 years assuming that the trend continues what will the population be af

The population of the Midwest industrial town decreased from 224,000 to 219,000 in just 2 years assuming that the trend continues what will the population be after an additional 5 years?
The population will be about?

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Jeniffer O. | I excel at the sciences!I excel at the sciences!
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First find the difference between the two initial sums: 224,000-219,000 = 5,000.  This is the decrease over two years.  Divide this by two to get the approximate decrease for one year.  5000/2 = 2500.  Multiply this times 5 years: 2500*5= 12,500.  Now subtract that from the last reported population: 219,000 - 12,500 = 206,500.
MANNY C. | 200+ Testimonials-Most Recommended Wyzant Tutor in USA.200+ Testimonials-Most Recommended Wyzan...
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Two ways:

Straight line Decrease and Exponential decrease.

In real life it will be exponential decrease.

224000*(1-x)^2 = 219000

(1-x)^2 = 219000/224000 = .9772

1-x =sqrt(.9772) = .9885

5 YEARS LATER:

219000*.9885^5=206693.8

Sharon T. | Mrs. Sharon T.Mrs. Sharon T.
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I first set up the equation as a ratios. I need to find the differences between the decline in population and the decline in years.  The decline in population went from 224,000 to 119,000, which is a decline of 5,000 after 2 years, which is expressed as:

5,000   X (Decline in population after 5 years)
2 years                        5 years

When you cross multiply, you get:  2X = 25,000
X = 12,500
That is not the answer yet. X is the decline in population which must be then subtracted from the current population of 219,000.

219,000 - 12,500 = 206,500
James P. | Science and Math can be your best subjectsScience and Math can be your best subjec...
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This question relates to geometric sequences, where the nth term (An) is related to the first term (Ao) by the expression An= Ao(rn)

In the question, n equals the number of years (2) over which the population has been measured, so the question tells us that:

A2 = Ao(r2)       where 2 = number of years, Ao = 22400, A2 = 219000 and n = 2. That is,

219000 = 224000r2

r = (219000/224000)1/2

We are asked to find the population a further five years after it reaches 219000, i.e. 7 years after it was at 224000

A7 = Ao(r7)

A= 224000

r7 = (219000/224000)7/2

A7 = 224000(219000/224000)7/2

A7 = 206980

This is equivalent to 207000 given the accuracy of the data in the question

This result is easily checked on any graphic calculator.
Denise V. | Patient and Knowledgeable who makes learning FUNPatient and Knowledgeable who makes lear...
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I found the answer this way what percentage of the population decreased 219,000/224000= .977% or a difference of 2% over 2 years knowing that then population should decrease another 5% in 5yrs because it was averaging 1% per year.
so 219,000 * 95%=208,050 is your answer.