While working on his science fair project, julian noticed changes in the cultures he was growing. he noticed that the cultures were increasing daily as displayed in the chart.
the rate is

1 day to 4 cultures
2 days to 9 cultures
3 days to 16 cultures
4 days to 25 cultures
if the increase continues at the same rate, how many cultures will be present on the ninth day?

The answer is:  " 100 cultures " .

   Take the number of the day we are at (from the beginning;  in this case, "9" (for "Day 9").

 Then add "1" to that number (in this case, " 9 + 1 = 10" .

Then, take that value (in this case, "10"); and "square" that value ; (in this case;  " 10² = 10 * 10 = 100 .   This is the answer.

The answer is:  " 100 cultures " .

Note:  We get this steps by noticing the trend from the information provided.