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!

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

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

This question relates to geometric sequences, where the nth term (A_{n}) is related to the first term (A_{o}) by the expression A_{n}= A_{o}(r^{n)}

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

A_{2} = A_{o}(r^{2}) where 2 = number of years, A_{o} = 22400, A_{2} = 219000 and n = 2. That is,

219000 = 224000r^{2}

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

A_{7} = A_{o}(r^{7})

A_{o }= 224000

r^{7} = (219000/224000)^{7}^{/2}

A_{7} = 224000(219000/224000)^{7}^{/2}

A_{7} = 206980

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

This result is easily checked on any graphic calculator.

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.

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