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I'm at a problem in a review section how exponential regression capability and I am...

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rrogers31 | Student, Undergraduate | eNotes Newbie

Posted January 26, 2012 at 3:45 AM via web

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I'm at a problem in a review section how exponential regression capability and I am unsure how to solve?

The table gives the population of a country, in millions, for the years 1900-2010.

Year       Population       Year        Population
1900                76        1960                179
1910                94        1970                207
1920                107      1980                224
1930                125      1990                252
1940                138      2000               289
1950                156      2010                319

Use a graphing calculator with exponential regression capability to model the population (in millions) since 1900. (Let t represent the number of years since 1900. Round your coefficients to five decimal places.)
P = ______________

Use the model to estimate the population in 1925. (Round your answer to the nearest whole number.)
____________ million people

Predict the population in the year 2020. (Round your answer to the nearest whole number.) ____________million people

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted October 15, 2012 at 3:16 AM (Answer #1)

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First you have to obtain a graphing calculator with regression capabilities. You could use a spreadsheet application also. The following is done on a TI-83 calculator:

Enter 10,20,...,110 into a list and the corresponding populations 76,94,...,319 into another list.

Then use the calc function in the stat menu to perform the expreg on the two lists.

The result is y=a*b^x where a=82.14509, b=1.01272 with a coefficient r=.99746 (the closer to 1 that r is, the better the fit)

So P=82.14509*(1.01272)^x

In 1925, t=25 so P=82.14509(1.01272)^25=112.7 so approximately 112.7 million

In 2020 t=120 so P=82.14509(1.01272)^120=374.4 so approximately 374.4 million

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