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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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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)
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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