Answer
(a) $y = 0.002x3 - 0.1045x2 + 1.9662x + 1.4558$
(b) See graph.
(c) $41$
(d) $2.0s$.
Work Step by Step
(a) Find the cubic polynomial that best fits the data.
$y = 0.002x3 - 0.1045x2 + 1.9662x + 1.4558$
(b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data.
See graph.
(c) Use your result from part (b) to estimate the number of vegetables that subjects would be able to name in 40 s.
When $x=40s$, we can find $y=40.9\approx41$
(d) According to the model, how long (to the nearest 0.1 s) would it take a person to name five vegetables?
When $y=5$, we can find $x=2.0s$.
