Question

Find the total cost of producing 5 camera cases.

Answer 1

Answer: c(x) = 7x² - 3b + 5

Step-by-step explanation:

c(x), making x camera cases is a quadratic function in terms of x:

c(x) = ax²+bx+c

c(2) = a2²+b.2+c = 27

c(4) = a4²+b.4+c = 105

c(10) = a10²+b.10+c = 675

4a+2b+c = 27

16a+4b+c = 105

100a+10b+c = 675

c = 27 - 4a - 2b

16a+4b+27-4a-2b = 105

100a+10b+27-4a-2b = 675

12a+2b = 78 (x-4)

96a+8b = 648

-48a - 8b = -312

96a + 8b = 648

48a = 336

a = 7

12.7+2b = 78

84 + 2b = 78

2b = -6

b = -3

c = 27 - 4.7 - 2.(-3) = 27 - 28 + 6 = 5

c(x) = 7x² - 3b + 5

Answer 2

We can translate the given problem into a table containing the data expressed as
x  c(x) ($)2   274   10510  675
to find the total cost of producing 5 cases, we plot first the data and find the equation. The equation is  c(x) = 7x2 - 3x + 5. when x is equal to 5, then c(x) is equal to $165