Question

in 2004, 510,000 acres of farmland in region were devoted to growing nuts. by 2011, the number of acres used to grow nuts had increased to 830,000. find the avarage rate of change in the number of acres in a region used to grow nuts from 2004 to 2011

Answer 1

Answer: 45714 per year.

Explanation:

Given : In 2004, 510,000 acres of farmland in region were devoted to growing nuts. by 2011, the number of acres used to grow nuts had increased to 830,000.

Change in acres of farmland from 2004 to 2011 = 830000-510000=320,000

Change in year = 2011-2004=7

The average rate of change is given by :-

`\frac{\text{Change in acres of farmland}}{\text{Change in year}}\\\\=(320000)/(7)=45714.2857143\approx45714 \text{[Rounded to the nearest integer.]}`

Hence, the average rate of change in the number of acres in a region used to grow nuts from 2004 to 2011 is 45714 per year.

Answer 2

Consider the (x, y) coordinates to be: (2004, 510000) and (2011, 830000).

Average rate of change is another name for slope, So, use the slope formula:
`m = (y2 - y1)/(x2 - x1)`

`m = (830,000 - 510,000)/(2011 - 2004)`

`m = (320,000)/(7)`

Answer: 320,000 acres every 7 years