The number of students admitted to sunshine school increases by 3% every year. in 2010, 697 students were admitted. which equation can be used to find the number of students admitted in the mth year after 2010?

The initial number of students is 697.
The increase is 3%. This means that the following year will be,
(100 + 3)% of the previous year. 
This is a geometric progression where common ratio can be calculated as follows;

1st term a = 697
2nd term = 103% of 697 = 717.91 

common ratio = (717.91/697) = 1.03.
So, the 2nd term = 697(1.03)∧1
The third term = 697(1.03)² 
The 4th term = 697(1.03)³

From the trend it can be seen that the previous term is given by a(r)∧(m-1),
where a⇒1st term
           r⇒common ratio and
          m⇒ is the term been calculated. 

∴This will give the equation for finding the number of students admitted in the mth year after 2010 as;
 
ar∧(m-1)

697(1.03)∧(m-1)

Whose mistake? can you give more details to what the question is asking?