Question

The number of vehicles a certain car dealership sold since January can be modeled by the function N(t) = 12t + 4 and the price per vehicle can be modeled by P(t) = 2.5t2 - 10 t + 45, where t is the number of months since January. Find a model to represent the total amount of revenue generated by the car dealership's sales in any month since January. (Revenue = Price * Cost)

do you multiply both equations ?

Answer 1

@phi

Answer 2

@whpalmer4

Answer 3

@ganeshie8 @thomaster

Answer 4

@d3Xter

Answer 5

@HelpBlahBlahBlah

Answer 6

Is the problem copied exactly as it appears in your text or assignment sheet or whatever? I ask because there is at least one incorrect statement (Revenue=price*cost) and a strict reading of the problem suggests a fairly complicated answer is being requested.

Answer 7

The number of cars sold in month \(t~~( t\ge1)\) will be N(t) - N(t-1) — all the cars sold to date, less all the cars sold prior to the beginning of the current month. We have to do this because the formula does not directly give us the number of cars sold in the current month, only the total number of cars sold since the start of January.

Because the formula for \(N(t)\) is that of a straight line, that reduces to a simple quantity, namely the slope of the straight line.

Now to find the revenue for a given month, we multiply the number of cars sold in that month by the price per car, given by \(P(t) = 2.5t^2-10t+45\). That's kind of a wacky pricing scheme, given that cars sold at the end of the year will be about 5x as expensive as cars sold at the start of the year!