The table gives the midyear population of Norway, in thousands, from 1960 to 2010. YearPopulation1960358119653723197038771975400719804086198541521990424219954359200044922005462520104891 Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. [Hint: Subtract 3500 from each of the population figures. Then, after obtaining a model from your calculator, add 3500 to get your final model. It might be helpful to choose t=0 to correspond to 1960.]

Question

The table gives the midyear population of Norway, in thousands, from 1960 to 2010.  YearPopulation1960358119653723197038771975400719804086198541521990424219954359200044922005462520104891  Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. [Hint: Subtract 3500 from each of the population figures. Then, after obtaining a model from your calculator, add 3500 to get your final model. It might be helpful to choose t=0 to correspond to 1960.]

Arham Warner · Accepted Answer

Step 1 Following the suggestions given by the problem, let t= the number of years after 1960 (so t=0 is 1960) enter the population numbers with 3500 subtracted from each. Using Desmos, first add a table. (clic on &quot;+&quot; at the upper left) and enter the numbers. It should look something like in this image: Step 2 x1y103581−350053723−3500103877−3500154007−3500204086−3500254152−3500304242−3500354359−3500404492−3500454625−3500504891−3500 Step 3 Next, you can get an exponential form y=abx by typing in the next box below the one with the table: y1 → ∼ a bx1 The values for a and b appear below. It should look similar to what is the image below. The model with the proper variable names and shifted back up by 3500 would be: P(t)=260.704(1.03408)t + 3500 Next in another box below, type this to get a logistic model: y1→ ∼ /M ↓ 1 + A e−kx1 It tells you the values of M, A, k below. P(t)2251.291 + 9.52066e−0.0522401t + 3500 Step 4 y1 ∼ abx1 R2=0.9624 e1 a=260.704 b=1.03408 y1 ∼ M1 + Ae−kx1 R2=0.9712 e2 M=2251.29 e2 k=0.0522401 Step 5 Neither model fits exactly, both stay reasonably close to the data points.

Suppose that you repeatedly shake six coins in your hand anddrop them on the floor. Construct a table showing the number ofmicrostates that correspond to each macrostate. What is theprobability of obtaining (a) three heads and three tails, and (b) six heads?

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