Question 1028726
your data is as follows:
<pre>
year       trees      difference     difference per year

1988        582
1989        620           38                38
1990        658           38                38
1992        734           76                38
1995        848           114               38
1997        924           76                38
</pre>


your growth is 38 years per year.
that's a straight line growth.
it fits a straight line equation.
the general form of that equation is y = mx + b
m is the slope
b is the y-intercept.


y is equal to the number of trees.
x is equal to the year from 1988.
1988 means x = 0
1989 means x = 1
etc.


your slope is the change in y divided by the change in x.
when the year changes by 1, the number of trees increased by 38.
your slo0pe is 38.


your equation becomes y = 38x + b
you can take any coordinate of (x,y) to find b.
just replace y with the number of trees and x with the year from 1988.
for example.
in 1988, the number of trees is 582.
x = 0 when the year is 1988.
y = 582 when x = 0
your coordinate point is (0,582)


in the equation of y = 38x + b, replace y with 582 and x with 0 to get 582 = 0 + b.
this results in b = 582.


your equation is y = 3x + 582.


as a test, use the year 1997.
when the year is 1997, x is equal to 1997 - 1988 = 9
when x = 9, y = 38*9 + 582 = 924
this agrees with what your are given, so the formula looks good.


when the year is 2020, x is equal to 2020 - 1988 = 32.
the number of trees is equal to y which is equal to 32*38 + 582 = 1798


when the year is 2088, x is equal to 2088 - 1988 = 100.
the number of trees is equal to y which is equal to 100*38 + 582 = 4382.
the city will not have 5000 trees by 2088 at the growth rate of 38 trees per year.