Product Rule Word Problem

[clw9110]

I am having a hard time with a product rule word problem:

If a farmer is farming 500 acres of corn in the current year and is increasing that number by 50 acres per year. He is currently harvesting 130 bushels of corn per acre, but the yield is increasing by 5 bushels per acre per year. When both the increasing acreage and the increasing yield are considered, how rapidly is the total number of bushels of corn increasing per year?

Any kind of guidance would help..

Thank you

 

[stapel]

If a farmer is farming 500 acres of corn in the current year and is increasing that number by 50 acres per year. He is currently harvesting 130 bushels of corn per acre, but the yield is increasing by 5 bushels per acre per year. When both the increasing acreage and the increasing yield are considered, how rapidly is the total number of bushels of corn increasing per year?

Try starting with what you learned back in algebra. If "t" is the year, with "last year, being the baseline" being "t = 0" so "this fall's harvest" will be "t = 1", what expression stands for "the baseline acreage, plus another fifty acres each year"? What expression stands for "the baseline per-acre volume, plus another five bushels per acre each year"?

The total yield is obviously (how many acres)*(how much per acre). So what expression stands for the total yield in year "t"?

Create the "yield" function, and then apply calculus to the result.