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 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?

Given the number of students 697. Since the increase is 3%, therefore each term will have to be multiplied by 100%+3%=103%

2nd term is (697) (103%) = 717.91

To ge the ratio:

= (717.91/697) = 1.03.

The formula is given by:

an = (a1) (r) ^ (n-1)

where:

a1 is the 1st term

r is the common ration is the term been calculated.

In this type of problem, the best equation to be use is the geometric progression formula, which is given by:

an = (a1) (r) ^ (n-1)

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)