Identifying a possible non-linear rule for a given table of values

Further examples of identifying a non-linear rule for a given table of values

Question 3

t	1	3	10	15
m	7	23	205	455

Which equation possibly describes the relationship between m and t ?

m = 6t + 1, m = −2t² + 5, m = 2t² + 7, m = 2t² + 5

Solution

Use substitution as the t values are not increasing by the same amount.

Option 1:	m = 6t + 1
	When t = 1, m = 7
	When t = 3, m = 19 ≠ 23
Option 2:	m = −2t² + 5
	When t = 1, m = 3 ≠ 7
Option 3:	m = 2t² + 7
	When t = 1, m = 9 ≠ 7
Option 4:	m = 2t² + 5

This has to be the answer.

Further example, Q2

Further example, Q4