The climactic moment in the film The Eggplant That Ate New

Chapter 2, Problem 2.44

(choose chapter or problem)

The climactic moment in the film “The Eggplant That Ate New Jersey” comes when the brilliant young scientist announces his discovery of the equation for the volume of the eggplant:

\(V\left(\mathrm{ft}^{3}\right)=3.53 \times 10^{-2} \exp \left(2 t^{2}\right)\)

where t is the time in hours from the moment the vampire injected the eggplant with a solution prepared from the blood of the beautiful dental hygienist.

(a) What are the units of \(3.53 \times 10^{-2}\) and 2 ?

(b) The scientist obtained the formula by measuring V versus t and determining the coefficients by linear regression. What would he have plotted versus what on what kind of coordinates? What would he have obtained as the slope and intercept of his plot?

(c) The European distributor of the film insists that the formula be given for the volume in \(\mathrm{m}^3\) as a function of \(t(\mathrm{~s})\). Derive the formula.