Each year for 4 years, a farmer increased the number…
This problem is testing us on exponential growth. The easiest way to navigate this problem is to set up a growth chart. We are given that the number of trees increased by ¼ each year. To determine the number of trees in a certain year, we multiply the number of trees from the previous year by 1.25, or 5/4. Let’s let x equal the number of trees at the beginning (of the first year) of the 4-year period.
We are given that there were 6,250 trees at the end of year 4 so we can set up the following equation:
(625/256)x = 6,250
625x = 6,250(256)
x = 10(256) = 2,560
Thus, there were 2,560 trees at the beginning of the 4-year period.