p(x) = 9.41 -0.19x + 0.09x2
dp/dx is the derivative of p with respect to x (w.r.t)
This is the average rate of change of price x years after 1990
dp/dx = d/dx(9.41 - 0.19x + 0.09x2)

=d/dx(9.41) + d/dx(-0.19x) + d/dx(.09x2)
= 0 + (-0.19) + 2 * 0.09 * x
= -0.19 + 0.18x
ans a) is dp/dx = -0.19 + 0.18x
Now that you know dp/dx ,you can now calculate the average rate of change of price for any year after 1990
Ans b) We need to find the price in 2010 that is 20 years after 1990.So our 'x' value is 20 .
Plug in 20 for x in p(x)
p(20) = 9.41 -0.19(20) + 0.09(400)
= 9.41 - 3.8 + 36
= 45.41 - 3.8
= 41.61
Please check the values again with your calculator
Ans c) Now plug in x = 20 on dp/dx
(dp/dx)when x = 20 = -0.19 + 0.18(20)
= -0.19 + 3.6
= 3.41

Jan 26th, 2015

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