Question

Can someone check my answer I got please.
Dorn Dairy has determined that the cost, in dollars, to produce and store g, in thousands of gallons, of milk is given by C(g).
Interpret in a sentence what C'(30)=0.4 means.

Answer 1

I got
It will take 30 thousands of gallons will be produced and stored and it will cost 0.4 dollars to do so.

Answer 2

C(g) is the cost to store g thousand gallons of milk

Answer 3

C'(g) is the rate of change of C(g)

Answer 4

C ' (g) is the instantaneous rate of change of the cost when you're storing g thousand gallons of milk

Answer 5

Yes to inkyvoyd

Answer 6

So if you were given C(30) = 0.4, then the interpretation of

"It will take 30 thousands of gallons will be produced and stored and it will cost 0.4 dollars to do so"

is correct

Answer 7

but you were given C ' (30) = 0.4

Answer 8

Use what jim said, and replace numbers for variables, and you will hav eyour answer :)

Answer 9

So then the answer is
It will cost 0.4 dollars for every 30 thousand gallons produced and stored.

Answer 10

No.

Answer 11

Rate of change would cost 0.4 dollars for every 30 thousand gallons produced and stored.

Answer 12

The derivative of cost is called "marginal cost" in economics.

Answer 13

close, but no, more like

when you store 30 thousand gallons, the instantaneous rate of change of the cost is $0.40 per gallon

Answer 14

oh ok I understand now I sort of had it I just needed a few different words.

Answer 15

oh sry, I meant to say $0.40 per thousand gallons

Answer 16

ok I got it.

Answer 17

essentially what this means is that at 30,000 gallons, if you add on more gallons (say 1000 gallons), then you're adding on roughly $0.40 (since the rate of change near 30,000 is $0.40 per thousand gallons)

keep in mind that once you get away from 30,000 the rate may change completely

Answer 18

ok got it thanks

Answer 19

@jim_thompson5910 because the rate of change CHANGES :o

Answer 20

yes exactly