A certain business has implemented a new incentive plan whereby employees earn tokens for every sale they make.
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
