Linear formula for cost (c) of waste collection as a function of number of gallons of waste (w)

Question

Is this really a linear formula? For 36 gallons, C = .25w, for 64 gallons, C = .201875w... That seems exponential or something funky is up with it. Can someone help me solve for C? Thanks

 

In a California town, the monthly charge for waste collection is $9 for 36 gallons of waste and $12.92 for 64 gallons of waste.

(a) Find a linear formula for the cost, (C), of waste collection as a function of the number of gallons of waste, (w).

C=?

Answer 1

INDEED, this is a poorly written problem.  Two differing formulas seem to be given.  Neither of them is exponential, however (if that were the case, the variable would appear in an exponent).

 

If you regard this as simply two given points (36,9) and (64,12.92), then you can use the point-slope form of equation (after computing slope m) to write the linear function that contains those two points.

 

But you have here a situation where the problem is over-specified, and in fact with conflicting information.

 

I SUSPECT COMMON CORE is at the core of this MESS. And you can tell your teacher that I said so.