Please answer each question thoroughly and detailed so I can understand since this is a practice problem that will be on my future exam. The values on the right will be needed to obtain the answers on the left. If values can't be seen, please zoom in a bit. I appreciate the help, thank you so much.
Introduction: The top 10 countries, emitters of CO2 starting from the first one, China. We will focus on the top two, China and the United States in this project.
United States (CO2 mmt) China (CO2 mmt)
4756 1597
4637 1587
4404 1671
4384 1786
4613 1948
4605 2067
4616 2140
4776 2260
4998 2406
5085 2413
5038 2417
4993 2460
2541 5186
2731 5263
2916 5324
3140 5518
3240 5589
3144 5637
3132 5700
3248 5889
3483 5778
3615 5820
3857 5886
4469 5994
5398 6007
6120 5929
6751 6016
7058 5823
7505 5404
8204 5594
9004 5455
9893 5236
10479 5359
10732 5414
10654 5262
10427 5169
10262 5151
10415 5278
10606 5147
10771 4580
10842 4904
11420
Per Capita Emission (metric tons per U.S. Population, China Population (metric tons per person)
223140018 982372466 21.3139715 71.6256563
225654008 997259502 20.5491586 1.5913611
228001418 1013483166 19.3156693 1.6487693
230389964 1029226907 19.0286066 1.7352830
232766280 1044172197 19.8181626 71.8655926
235146182 1060239979 19.5835627 1.9495586
237512783 1077770523 19.4347434 1.9855803
239853168 1096851843 19.9121822 71.0604423
242287814 1115889802 20.6283589 72.1561268
244954094 1134414723 20.7589916 72.1270880
248083732 1153704252 20.3076596 72.0949909
251560189 1170626171 19.8481326 72.1014394
255175339 1183813389 19.9627441 72.1464531
258779753 1195855558 20.0402077 72.2837206
262273589 1207286675 20.0668318 72.4153335
265660556 1218144426 20.0406115 72.5776910
268984347 1228298836 20.5142048 72.6377945
272395438 1237801448 20.5179647 72.5399873
275835018 1246836105 20.4361289 72.5119580
279181581 1255433236 20.4168196 72.5871547
282398554 1264099069 20.8535062 72.7553220
285470493 1272739582 20.2402705 72.8403296
288350252 1280926120 20.1837867 73.0111026
291109820 1288873367 20.2191736 73.4673693
293947885 1296816711 20.3913697 74.1625003
296842670 1304887562 20.2363090 74.6900592
299753098 1313086567 19.7796120 75.1413213
302743399 1321513224 19.8716141 75.3408470
305694910 1330167148 19.0484035 75.6421480
308512035 1339125595 17.5163344 76.1263857
311182845 1348191368 17.9765693 76.6785771
313876608 1357095481 17.3794410 77.2898334
316651321 1366560818 16.5355381 77.6681548
319375166 1376100308 16.7796390 77.7988500
322033964 1385189668 16.8118913 77.6913654
324607776 1393715448 16.2103325 77.4814410
327210198 1401889681 15.7971849 77.3201195
329791231 1410275957 15.6189720 77.3850794
332140037 1417069468 15.8908876 77.4844601
334319671 1421864031 15.3954446 77.5752672
335942003 1424929781 13.6333056 77.6087959
336997624 1425893465 14.5520313 78.0090134
Consider the data in the Microsoft Excel sheet. Use it to answer the questions. It will be easier to use Excel to do the calculations and attach the file to the project, but write the answers directly in the space provided here. Click here for the spreadsheet.
Calculate the average rate of change of total emissions from 1980 to 2021 for the USA and China. Give a brief summary and the practical meaning of your results.
Use the Intermediate Value Theorem to show that there exists a year where the USA and China produced the same amount of CO2 using the mathematical models provided. You will have to carefully select the interval. As a hint, use the given graph.
Sometimes we want to find a result in a small interval about a specific value for a very complicated function. To save time, we can locally linearize the function and use the linearization to approximate the value. This is very useful if we are interested in a specific result. For example, the data in this project was collected annually. How might we approximate the amount of CO2 emitted on a specific day during a given year? Let's try it. Use local linearization of f about t = 40 to approximate the amount of CO2 emitted on a specific day.