Graphs of Functions

  1. Based on data from the Bureau of Transportation Statistics, the function ff below models US sales (in thousands) of electric and plug-in hybrid vehicles after the year 2000. f(t)=−0.573822t2+36.7706t+1.35449 f(t) = -0.573822t^2 + 36.7706t + 1.35449

    1. Sketch a graph of y=f(t)y = f(t) on a viewport where the minimum and maximum values of tt correspond to the years 2000 and 2050. What minimum and maximum values of yy do you need to get a “good” view of the graph?
    2. Interpolate: according to the model ff 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.
    3. Extrapolate: according to the model ff 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.
    4. Estimating, based on the graph of the model, what year will US sales of electric vehicles begin declining?
    5. Is this a reasonable model for years before 2000? What about for years after 2050?