word problem regarding dy/dx

[kris17]

A group of biology researchers showed that the number of eggs (y) that a certain insect lays on a mungbean plant could be approximated by y=-57.4+63.8x-20.8x^2+2.4x^3, where x is the age of the mungbean plant in years, for 2≤x≤7 . Which is the best interpretation of
dy/dx?


a) The number of eggs on the plant after x years.
b) The number of years it takes for the plant to accumulate y eggs.
c) The time expected for the insect to lay one more egg .
d) The additional number of eggs expected on the plant in year 7 compared to year 2.
e)The rate at which the eggs are accumulating or dropping off at a given point of time

I picked A, just because thats what I personally interpreted it as.but im having doubts, thinking it might be d. Any input??

 

[Deleted member 4993]

A group of biology researchers showed that the number of eggs (y) that a certain insect lays on a mungbean plant could be approximated by y=-57.4+63.8x-20.8x^2+2.4x^3, where x is the age of the mungbean plant in years, for 2≤x≤7 . Which is the best interpretation of
dy/dx?


a) The number of eggs on the plant after x years.
b) The number of years it takes for the plant to accumulate y eggs.
c) The time expected for the insect to lay one more egg .
d) The additional number of eggs expected on the plant in year 7 compared to year 2.
e)The rate at which the eggs are accumulating or dropping off at a given point of time

I picked A, just because thats what I personally interpreted it as.but im having doubts, thinking it might be d. (both incorrect)Any input??

How would you interpret δy ? →change in y (within a given domain)

How would you interpret δx ? →change in x (within a given range)

How would you interpret δy/δx ? →change in y for a given change in x [in your case that would be (change in # of eggs)/(change in time)]

How is δy/δx and dy/dx related?

 

[HallsofIvy]

You see to be mistaking the "derivative" for the "integral". The derivative is a "rate of change", not an accumulated value.

 

[kris17]

ahh makes sense. so them Im guessing E would represent that best.

 

[Deleted member 4993]

ahh makes sense. so them Im guessing E would represent that best. CORRECT

.

 

[HallsofIvy]

ahh makes sense. so them Im guessing E would represent that best.

That's correct but you need to stop guessing! Learn the definitions and concepts, not just the formulas.