The cost, C (in dollars) to produce g gallons of ice cream can be expressed as C

Question

The cost, C (in dollars) to produce g gallons of ice cream can be expressed as C=f(g).

(a) In the expression f(300)=325,
what are the units of 300?    ?    dollars    gallons    dollars*gallons    dollars/gallon    gallons/dollar   
what are the units of 325?    ?    dollars    gallons    dollars*gallons    dollars/gallon    gallons/dollar   

(b) In the expression f(300)=1.4,
what are the units of 300?    ?    dollars    gallons    dollars*gallons    dollars/gallon    gallons/dollar   
what are the units of 1.4?    ?    dollars    gallons    dollars*gallons    dollars/gallon    gallons/dollar   

(Be sure that you can carefully put into words the meanings of each of these statement in terms of ice cream and money.)

Explanation / Answer

C = f(g) = f(300) = 325

So, cost is 325 and g = 300

So, units of 300 is : gallons ----> ANSWER

And units of 325 is : dollars ---> ANSWER

This means,
"The production cost of 300 gallons of ice-cream is 325 dollars"

----------------------------------------------------------

C'= f'(300) = 1.4

Again here, the 300 is in gallons

So, units of 300 is : gallons ----> ANSWER

When we derive, we are dividing C/g, i.e dollars per gallon

So, units of 1.4 is : dollars per gallon ----> ANSWER

This means,
"Rate of change of production cost with respect to the
number of gallons of icecream when the number of gallons of
icecream is 300 is equal to 1.4 dollars per gallon"

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.