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Problem 35 Hard Difficulty

Use a graphing calculator with exponential regression capability to model the population of the world with the data from 1950 to 2010 in Table 1 on page 49. Use the model to estimate the population in 1993 and to predict the population in the year 2020.

Answer

Population estimated for $1993 : \approx 5381$ millions of people.
Population predicted for $2020 : \approx 8466$ millions of people.

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Video Transcript

all right for this problem we're using the data from the table on page 49 were using some of the data for the populations from 1950 to 2010. So we go into our stat menu and then into edit, and we type those numbers in from the year 1950 onto the year 2010 and those populations that correspond. Now we want to use the calculator to find the exponential regression equation. So we go to stat and then over to calculate when we go down, until we find exponential regression. So we select that we're using list one and list, too. And we do want to store the regression equation in our y equals menu so that we can use it to make predictions and estimates. So we're going to store that in why one. So we go to variables and then over toe y variables select function and select why one now we can calculate. Okay, so the exponential regression equation is approximately y equals 1129.2 times 1.1 to the X. And if we press, why equals we see that that equation has been pasted in. Now we want to use that to estimate the population in 1993. So let's go ahead and go to table set and make sure that our settings air set to independent ask, which will allow us to type in which ever X value we want. And now we'll go to table, which is second graf and we're going to type in 93 to represent 1993 and we end up with 5380.6 and that would be in millions, the population in millions. And then we also want to make the prediction for the year 2020. So we type in the year 1 20 to stand for 2020 and we get 8466 million, which would be 82.466 billion