Hi I’m can I please receive homework help as soon as possible please thank you

Question

Using an exponential model for the data, estimate when the population will exceed 100 million.

A.) The population will exceed 100 million in 2022.

B.) The population will exceed 100 million in 2011.

C.) The population will exceed 100 million in 2017.

D.) The population will exceed 100 million in 2008.

Answer 1

To find the "best fit" of the data is called exponential regression and this is NOT EASY to do manually. The best way to do this is with a calculator. If you have a TI-84, you can put this data into a list and then at the push of a button you'll have the answer. If you don't, you can use a tool like Desmos to do it in the same way. I'll assume you have a TI-84.

First make sure your stat diagnostics are turned on. Do this by pushing the catalog button (Blue then Zero) and scroll all the way down to "DiagnosticOn". Select it then hit enter again to execute it. The screen will say "Done"

Now, enter the data into your list table by pushing the "stat" button (it's 4 buttons up from the "8") then enter when "EDIT" is highlighted ("EDIT" is highlighted after you push "stat" so pushing "stat" then "enter" is what you want). You will be on the List entry page. In the L1 column, enter your "x-values" but, in your case, assume the year 2000 is year zero so enter 0, 2, 4, and 6. Then in the L2 column, enter the y-values: 53, 57, 62, and 67. The get back to your main screen by pushing quit (Blue mode).

Now calculate the equation you are looking for by pushing "stat" then scroll right to "CALC" then scroll down to "10:ExpReg" and hit "enter". The "Xlist" should say "L1" (that's where you put your "x-values" from your data) and the "Ylist" should say "L2" because that's where you put the y-values from your data. Scroll down to "Calculate" and hit "enter". The screen should say:

y=a*b^x

a=52.88923184

b=1.040149301

r²=0.9993007349

r=0.9996503063

This is the answer you are looking for. It is the equation of the exponential function that best fits the data. How good it fits the data is shown by the r2 and r values. The closer they are to 1, the better the fit. In this case they are very close to 1 so this is a good model.

To find out the correct answer, use the equation you got (y = 52.88923184(1.040149301)^x and plug in x = 22 (for 2022 to see what your model predicts the population as. (I got 125.7 million). Keep checking the other answers until you find one just a little more than 100 million.