Certain pieces of antique furniture increased rapidly in price in the late 1990’

Question

Certain pieces of antique furniture increased rapidly in price in the late 1990’s. For
example the value of a particular rocking chair was well approximated by
V = 75.(1.35)^t
where V is in dollars and t is the number of years since 1995. For each of the following
statements decide if it is true or false. Explain your reasoning.
(a) V(2)will be negative
(b) V(2) gives the value of the rocking chair in 1997
(c) V(2) gives the change in value of the rocking chair from 1995 to 1997
(d) V(2) gives the rate at which the value of the rocking chair was changing in 1997

Explanation / Answer

a)v'(t)= 75 (1.35)^t ln 1.35= 22.5078(1.35)^t v'(2)= 41.02 False. b) False since v'(2) gives the rate of change of the value in 1997 c) False since v'(2) gives the approximate change in value between 1997 and 1998. d) True, that's the definition of v'(2) the rate of change in the value in 1997 (since 1997 is 2 years after 1995).

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