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Based on data from the Bureau of Transportation Statistics, the function \(f\) below models US sales (in thousands) of electric and plug-in hybrid vehicles after the year 2000. \[ f(t) = -0.573822t^2 + 36.7706t + 1.35449 \]
- Sketch a graph of \(y = f(t)\) on a viewport where the minimum and maximum values of \(t\) correspond to the years 2000 and 2050. What minimum and maximum values of \(y\) do you need to get a “good” view of the graph?
- Interpolate: according to the model \(f\) how many US electric vehicle were sold in the year 2020? Find the point on the graph corresponding to this input/output pair and label it with its coordinates.
- Extrapolate: according to the model \(f\) how many US electric vehicle sales are predicted in the year 2050? Find the point on the graph corresponding to this input/output pair and label it with its coordinates.
- Estimating, based on the graph of the model, what year will US sales of electric vehicles begin declining?
- Is this a reasonable model for years before 2000? What about for years after 2050?