The values of certain types of collectibles can often fluctuategreatly over time. Suppose that the value of a particular limitededition figurine is found to be able to be modeled by thefunction
?(?) = ?0.01?4 + 0.47?3 ?7.96?2 + 49.18? + 65 for 0 ? ? ? 20 where ?(?) is indollars, t is the number of years after the figurine was released,and ? = 0 corresponds to the year 1999.
a) What was the value of the figurine in the year 2009?
b) What was the value of the figurine in the year 2019?
c) What was the instantaneous rate of change of the value of thefigurine in the year 2002?
d) What was the instantaneous rate of change of the value of thefigurine in the year 2019?
e) Use your answers from parts a-d to estimate the value of thefigurine in 2020.
