Question

Do you guys know the word problem about Food production, it goes like this "The table below shows pork production in China from 2000 to 2007." I saw the answer to this problem in this website but I wasn't quite sure where they got some of the answers

Answer 1

Hi and welcome to QuestionCove!
I did a quick Bing search for the problem you described.
Does it go something like this:

The table below shows pork production in China from 2000 to 2007.
Use a calculator to find the line of best fit.
b. Use your linear model to predict how many metric tons of pork will be produced in 2025 ...
c. Use your linear model to predict when production is likely to reach 100,000 metric tons ...
[Year: 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007.
Production (metric tons) : 40,475, 42,010, 43,413, 45,331, 47,177, 50,254, 52,407, 54,491

Answer 2

It seems you'd want to use a graphing calculator or some similar linear plotting tool in order to solve this problem. Once you have your line of best fit, parts b. and c. rely on extrapolation (extending the data outward to make predictions) and interpolation (filling in the gaps of data to account for unmarked points), respectively

Answer 3

The word problem had a table to I plugged those in on desmos. The equation I found on this website was y=2053.17x + 39759
I know the 2053.17x part, but I'm not sure where they got the 39759 from

Answer 4

As you probably understand, 2053.17x represents the growth of food production each year. We could think of that as meaning "on average, the tons produced increase by 2053.17 per year"
The 39759 is the y-intercept of the equation, which is what the value would be when x=0, or in this case, if we go back to the first year that the equation accounts for.
Notice that the first year production is 40,475, which is quite close to the y-intercept of 39,759. The line of best fit will not match up with the data points exactly, but it is quite close; this is sort of like an estimation for what the production levels were at the very beginning of the data in the table

Answer 5

Do you have an equation of how you got 39,759? bc i dont really get what u mean when you said that the first year production was close to 39,759

Answer 6

Here is a screenshot of my desmos which gave me the growth of food production each year

Answer 7

If you want to know exactly how the value of 39,759 was found for the equation, you can review the method and calculations for finding a line of best fit based on a set of data points here (least-square method) https://www.varsitytutors.com/hotmath/hotmath_help/topics/line-of-best-fit

In terms of understanding conceptually what 39,759 means for your line, this is saying that, based on the line of best fit you are using, the estimated amount produced would be 39,759 in the year 2000. This is different from the actual amount of 40,475 by about 800, but the estimated value is pretty close to the actual value; this is a good sign that the line of best fit somewhat represents the values of the existing data points

Answer 8

oh okay thank you so much I didn't expect for someone to actually reply to my problem

Answer 9

Similarly, 2053.17 growth rate is an estimate too; in some years, the production increases by more, and in some years it increases by less, but this is the rate which was calculated to be the best estimate--the best fit, based on the data points given.
It does seem like the actual calculations for finding this equation are a bit complicated, so that is probably why you are able to use a calculator for this problem.

And I'm glad to help, it's not a problem. If I'm able to help at all, then I'm glad :)

Answer 10

Oh, I almost forgot about the other parts of the question, now that you've found your line of best fit.

So, b. asks you to predict the production of pork in 2025. Using the equation of the best-fit line you found,
y=2053.17x + 39759
if x=0 corresponds to the year 2000, then x = 25 will correspond to the year 2025; simply plug "25" into the equation in place of x in order to get your estimate

For part c, to estimate what year production will reach 100,000, substitute y for 100,000 and then use algebra to solve for x, i.e.
100,000 = 2053.17x + 39759
Then, add the value you find for "x" to 2000 to get the estimated year, since "0" represents the year "2000" in this case

Answer 11

Yes I've already done those parts too. Thank you smokeybrown

Answer 12

Oh, wonderful. Glad you figured it out!