Question 267725
If {{{e}}} is the starting enrollment,
Let {{{n[y]}}} = number of students in year {{{y}}}
{{{n[1] = 5678 - .24*5678 + 1250}}}
{{{n[2] = (n[1] - 1250)*.24 + 1250}}}
{{{n[3] = (n[2] - 1250)*.24 + 1250}}}
But {{{n[2] - 1250 = (n[1] - 1250)*.24 }}}, so
{{{n[3] = ((n[1] - 1250)*.24)* .24 + 1250}}}
{{{n[3] = (n[1] - 1250)*(.24)^2 + 1250}}}
So, I can generalize:
{{{n[y] = (n[1] - 1250)*.24^(y-1) + 1250}}}
I can calculate {{{n[1]}}}
{{{n[1] = 5678 - .24*5678 + 1250}}}
{{{n[1] = 5678*.76 + 1250}}}
{{{n[1] = 4315.28 + 1250}}}
{{{n[1] = 5565.28}}}
In {{{6}}} years:
{{{n[6] = (5565.28 - 1250)*.24^(6-1) + 1250}}}
{{{n[6] = 4315.28*.24^5 + 1250}}}
{{{n[6] = 3.436 + 1250}}}
In 6 years there will be 1253 students
Hope this is right, and you understand
You can take it from there