College algbra: (regression Equation) depend on the chart how to find linear, exponential model?

cysh010

Do you have the document file available as well? Will make it easier when putting into Excel

Let me know!

3929214
5308483
7239881
9638453
12866020
17069453
23191876
31443321
38558371
50189209
62979766
76212168
92228496
106021537
123202624
132164569
151325798
179323175
203302031
226542199
248709873
281421906  
307745538

here ya go!


4) Let's take a closer look at our data. Using the regression feature on your calculator, find a linear model and
an exponential model and then answer the following questions. Round to the nearest thousandths.
Linear (y = mx+b)
Find the Linear Model (2 pts)
What is the correlation coefficient (r-value)? (l pt)
What is the slope from this model? (1 pt)
Interpret this value using the appropriate units. (2 pts)
What is the initial value from this model? (l pt)
Interpret this value using the appropriate units. (2 pts)
Exponential ( y = )
Find the Exponential Model (2 pts)
What is the correlation coefficient (r-value)? (l pt)
What is the rate of growth from this model? (l pt)
Interpret this value using the appropriate units.
What is the initial value from this model? (l pt)
Interpret this value using the appropriate units.
(2 pts)
(2 pts)

5) Predictions — based on each regression equation you found above, find the expected population in 2030,
2040, and 2050. Include units and round to the nearest thousandths. (6 points)
6) How do the values found by your "Lines of Best Fit" compare to the article's predictions in 2030, 2040, and
Linear
2030
2040
2050
Exponential
2030
2040
2050
Next determine what year the US population would reach I Billion. Round to the nearest year. (2 pts each)
1 Billion
2050? (6 pts)
1 Billion
Linear
Model
Prediction
in millions
How does the
Linear
Model
com are?
Exponential How does the
Year
2030
2040
2050
Article's
Prediction
(in millions)
355
373
388
Year
2030
2040
2050
Article's
Prediction
(in millions)
355
373
388
Model
Prediction
in millions
Exponential
Model
com are?
7) (a)What model matches the data points we have the best? (l point)
(b) What model do you feel is better for making predictions? Explain why? (2 points)
8) State two 'real world' events that impact population that the model does not take into consideration? These
events could cause populations to increase or decrease. (2 pts)

Thanks cysh010

So, after I plugged the data into Excel, I see this:



Notice that it doesn't look linear.

But if we use Excel's features, we get an R2 value of 0.9196. If we square-root that, we get the r value of 0.9589

The equation, as per Excel is: y = 13,593,427.71x - 59,181,395.13. The bold text indicates the slope, 13,593,427.71 people per every 10 years. If you want per one year, divide 13,593,427.71 by 10 = 13,593,42.77 people per year

Given that it is positive, that means this is a growth of 13,593,427.71 people every 10 years starting from the year 1790.

The initial value - not sure what that means here - is the year (0, 3,929,214). This could mean the meaning of the y-intercept of the equation provided above. In that case -45,587,967.41 follows the line of best fit that approximates the data. So if we follow the line of best fit, it suggests that the population was -45,587,967.41 at year 0 (1790). Clearly that makes no sense, but then again that what happens when you use a linear model to scale an exponential growth. The units would be people.

Is this making sense so far? Let me know before I continue...

i attached files

Okay, thanks...

Let's continue page 2.

Here's what the data looks like approximating it on Excel using the exponential model - exponential meaning that the value of 'b' is "e" ~ 2.7182:



Notice the R2 value is 0.9624. Square-root this number to get r: 0.9810. This number is closer to 1, which means that it's a better approximation than the linear data.

The rate is given as 0.1963 mentioned above.

y = 6,307,289.9243e0.1963x

The fact that 0.1963 is positive means that there is growth. 0.1963 is the decimal version of 19.63% per 10 years or... dividing them out: 1.963% per year.

To get the initial value for the exponential model, set x = 0:

y = 6,307,289.9243e0.1963(0)

you get: y = 6,307,289.9243

The units are "people" at year 1790.

Let's move onto page 3...

I'll have to revise my answers, because I did this quickly.

I'll look at it in a few hours again.

When's it due? Plus, have you learned about equations with the letter "e"?

Thank you very much and would you please help me the question 4 too??

it's due July 28th.. and I am learning about  equations with the letter "e" but It is very confuse me

Nice, you've come to the right place.

Here are the answers summarized for question #4

Let me know if you have any troubles.