Question

Quick computing company produces calculators they have found that the cost c(x),of making calculators is a quadratic function in terms of x.
The company also discovers that it costs $45 to produce 2 calculators, $143 to produce 4 calculators, and 869 to produce 10 calculators.

Find the total cost of producing 7 calculators.

Answer 1

A quadratic function is given by y = ax^2 + bx + c
c(2) = a(2)^2 + 2b + c = 45
4a + 2b + c = 45 . . . (1)
c(4) = a(4)^2 + 4b + c = 143
16a + 4b + c = 143 . . . (2)
c(10) = a(10)^2 + 10b + c = 869
100a + 10b + c = 869 . . . (3)

Solving (1), (2) and (3) gives a = 9, b = -5, c = 19

Therefore, c(x) = 9x^2 - 5x + 19
c(7) = 9(7)^2 - 5(7) + 19 = 9(49) - 35 + 19 = 441 - 16 = 425

Therefore, it costs $425 to produce 7 calculators.