The median home price in a country over the period January 2010 to January 2021 can be approximated by

P(t) =0.81t²0.42t+209thousand dollars (0t11),

wheretis time in years since the start of 2010.(a)Calculate the average rate of change of the median home price (in thousands of dollars per year) over the 5-year period beginning at the start of 2010_________. thousand dollars per year Interpret your answer (in dollars per year).The median home price was increasing at an average rate of about $ _______ per year over the 5-year period beginning at the start of 2010.(b)What, if anything, does your answer to part (a) say about the median home price in 2012? Explain.

The median home price for 2012 is going to increase by half of the amount in part (a).The median home price for 2012 is going to decrease by half of the amount in part (a). Nothing; the average rate of change of a function over [a,b] is not affected by values of the function betweenaandb.

(c)Complete the following table (in thousands of dollars per year). (Round your answers to three decimal places.)

h	1	0.1	0.01	0.001	0.0001
Avg. Rate of Change ofPover[10, 10 +h]

What do the results suggest about the rate of change of the median home price (in dollars) at the very beginning of 2020? [Hint: See Example 4.] (Round your answer to the nearest whole number.)Home prices were increasing at a rate of about $_________ per year at the very beginning of 2020.