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Problem 35 Medium Difficulty

The unemployment rate $ U(t) $ varies with time. The table gives the percentage of unemployed in the US labor force from 2003 to 2012.

(a) What is the meaning of $ U'(t) $? What are its units?

(b) Construct a table of estimated values for $ U'(t) $.

Answer

a) $U^{\prime}(t)$ represents the change in $\%$ of the employed population in the U.S. from 2003 to 2012.
b)

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Video Transcript

this phone number thirty five of this tour Calculus eighth edition Section two point eight The unemployment rate U of t varies with time. The table gives the percentage of unemployed in the US labor force from two thousand three to two thousand twelve. What is the meaning out You prime a team water its unit. So here we see the unemployment rate in percent of people unemployed. Ah, percent of people with district of the full population. That's the U. And we have that data for every year from two thousand three two thousand twelve. You promised he would be the derivative of you with respect to temper our two time so two year and therefore you promised. He represents the change in the unemployment rate. Ah, per year and it's units are percent of people unemployed her year. So we can definitely write that here Percent of people unemployed him, uh, per year. All right are being contract the table of estimated values for you prime of team. But here's an attempt at estimating the values of you. Prime Minister. Here's an example of what is being done for this here two thousand four. We're taking the average uh, the ray of change from two thousand three to two thousand four and the rate of change between two thousand four two thousand five. So essentially we were gonna have the next year, minus the first year, the change in the unemployment rate to bed about it one year on DH. That's one average rate of change. And then we're going to do that because here. So the unemployment rate, her the unemployment percent, someone here and then the reform, that difference of the unemployment rate to everybody. One air, which is the interval. And those two average rate of change is are averaged for each of the years and against us thes approximate rates of change for you, prime of team and at the end points. Since there's no information for before or after, then it's just are given as thie average sort of change with the data given from the year before or from the hereafter. So these air the estimates that we have come up with for the average or for the rate of change over the unemployment rate, uh, with respect to time per year,