help calculus question

[angelbravo2143]

A factory charges a manufacturing rate of ?(?)=4?−0.3?²+10 thousands of dollars per month. Determine the total price for using the factory for the first 3 months of operation. Give your answer in thousands of dollars. m=months

 

[Deleted member 4993]

A factory charges a manufacturing rate of ?(?)=4?−0.3?2+10C(m)=4m−0.3m2+10 thousands of dollars per month. Determine the total price for using the factory for the first 3 months of operation. Give your answer in thousands of dollars. m=months

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[Dr.Peterson]

A factory charges a manufacturing rate of ?(?)=4?−0.3?²+10 thousands of dollars per month. Determine the total price for using the factory for the first 3 months of operation. Give your answer in thousands of dollars. m=months

The problem seems a little ambiguous to me. It is written as if this rate were a continuous function, in which case integration (from 0 to 3?) would be appropriate; but a month is a discrete unit of time ("first three months"), so it may well mean that C(1) is the rate for the first month, and so on. In that case, we need a summation.

What topic is being taught? Has anything more been said about the meaning of the function? It would have been better if the variable m had been defined more precisely.

 

[Otis]

Ah, I'd thought the domain was continuous (missed "per"), and I'd misinterpreted the rate as well. (Didn't even know I was on the Calculus board, oops.)