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Tor Ehe foflowing data Shifc che pa9e Period 0 CPI frOC 1567 1970 Adjust the Eo 1978 constant dollar Which Ralazhe?/ Yea? che hlgheat chasing pover? Salary cPIUAL-Q...

Question

Tor Ehe foflowing data Shifc che pa9e Period 0 CPI frOC 1567 1970 Adjust the Eo 1978 constant dollar Which Ralazhe?/ Yea? che hlgheat chasing pover? Salary cPIUAL-QLL 1974 317,000 142.1 1976 518,500 164 - 1976 919 500 185 1980 523 S00 223

Tor Ehe foflowing data Shifc che pa9e Period 0 CPI frOC 1567 1970 Adjust the Eo 1978 constant dollar Which Ralazhe?/ Yea? che hlgheat chasing pover? Salary cPIUAL-QLL 1974 317,000 142.1 1976 518,500 164 - 1976 919 500 185 1980 523 S00 223



Answers

The average hourly wage (adjusted to 1982 dollars) was $\$ 8.46$ in 1970 and $\$ 8.18$ in 2005 (Source: Department of Commerce.) (A) Find an equation of a line that passes through the points $(1970,8.46)$ and $(2005,8.18)$ (B) Interpret the slope. (C) Approximate the hourly wage in 2000 . Compare the estimate to the actual value of $\$ 8.04$

Thanks. So, for part A, we have seen define G of 1970 pyre. So it's gonna look at 1975 on the left side of our table. So the minimum wage of 1975 is gonna be $2. Okay, Uh, part being just wants me to find the difference. O g of 1995 in 1975. Timorous attracting G of 1975 which was $2. Sergey of 1995 was $4.25. So the difference is gonna be $2.25. Okay. And so interpreting that. That means over those 20 years. So those 20 years, not any 20 years, a minimum wage went out. Uh, $2.25. Thank you very much.

So I have some information which corresponds toe the average our live it on the corresponding here. So the ordered pairs are given to me as one in 1990 year and $7.66 in the year 2009 it waas $8.27. So I have to find a slow point for the line which passes through these points. So first of all, if I talk about look, that is m is a corrido 8.27 minus 7.66 That is why to minus why one divided way 2009 miners 1990. So that comes out, Toby. So this value comes or Toby 0.61 divided when? 19. That is equal to 0.321 So there is a slope. Now you question off the line. I can write it as y minus Anyone value. I can pick up 7.66 I will take is equal to 0.321 There this spoke times x minus X one that is 1990 So that gives me why is it called 0.321 x on These are loose. If I simplify I'll bigger thing. I will be having this well us minus 56 point 219 So that is going to be my the question off the lane in point slope form. So next interpret the slope so I can say slope is equal to 0.321 This denotes the slope actually denotes the that it off Chan's off ridge buddy at so that is interpretation of the slope and ah, the same question I have to use to approximate the our live age in 2005 so x equal to 2005. Basically, they're asking me corresponding to that and the year 2005 I'll put X equal to 2005. So why will be 0.321 multiplied way 2005 minus 56.21 main So on calculating this I will have this value equals toe 8.1415 dollars. So that is where answer Onda. Comparing it with 8.1 ip So clearly the lady in 2000 claim is Ah Unless then 8.1 their dollars. Well, it So that's how we have done so I opened clear. Thank you

It was probably want to find the average rate of change in minimum wage during the different intervals. And we know that our average rate of change is going to be our change in minimum wage over our change in time. So for a part A. We need to first convert our, uh 1950 1976 in terms of the um X, which is zero corresponds to 1950. So we have f of 26 minus f of zero over 26 minus zero. And if we plug in the values we get 6.96 minus 5.36 over 26 in that equals $0.62 per year from part B. Our interval is from 1976 to 1995. So we need to convert that into X of 45 26. So we have f of 45 minus f of 26 over 45 minus 26 and so plugging in the values we get 4.80 minus 6.96 over 19 which equals negative $0.114 a year for part C. We have an interval from 1995 to 2000. So our X values are from, um, 50 and 45. So we have F 50 minus F of 45 over 50 minus 45 and plug in the values we get 5.15 minus 4.80 over five in that equals $0.7 per year. For Part D. Our interval is from 1976 to 2000. So our X values are from 26 to 50. So we have s of 50 minus F of 26/50 minus 26 which is 5.15 minus 6.96 over 24 and that is negative 0.75 dollars per year.

Because we aren't allowed to show the actual table here. Our goal for this problem is going to be to create a model. So here's what this looks like. We want to first start by um entering data or inputting data. President. Okay, great calculator or Excel. Then you want to select data. Yeah. And create a trend line on trend line. In Excel or aggression line is what it's called the calculator. And then you want to make sure you choose the correct model um um model um form or choose the correct general form. So what I mean by that is going to be it's going to be either a linear form exponential form um Depending on what the problem gives you. And with that form you will obtain the model. And the model is really what we're after. Because once we have the model we can interpret results, predict future outcomes um or determine outcomes of unknown data points. Really that is where modeling becomes a very huge and important aspect within math and science. Um


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