Question

A certain business has implemented a new incentive plan whereby an employee earns tokens for every sale they make. What is the formula to use?

Answer 1

For 1 sale, an employee earns 1 tokens.
For 2 sales, an employee earns 6 tokens.
For 3 sales, an employee earns 12 tokens.
For 4 sales, an employee earns 19 tokens. 

For the answer to the question above,
Suppose that for x sales the number of tokens the employee earns is: 
ax^3 + bx^2 + cx + d 
Therefore: 
a(1^3) + b(1^2) + c(1) + d = 1 
a(2^3) + b(2^2) + c(2) + d = 6 
a(3^3) + b(3^2) + c(3) + d = 12 
a(4^3) + b(4^2) + c(4) + d = 19 
Therefore: 
a + b + c + d = 1 
8a + 4b + 2c + d = 6 
27a + 9b + 3c + d = 12 
64a + 16b + 4c + d = 19 
Solve that to get: 
a = 0 
b = 1/2 
c = 7/2 
d = -3 
Therefore, the formula is: 
(1/2)x^2 + (7/2)x - 3