Quick Computing Company produces calculators. They have found that the cost, c(x), of making x calculators is a quadratic function in terms of x.
The company also discovered 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.
Stacey Warren - Expert brainly.com
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Quadratic function is
\[C(x) = ax^2+bx+c\]
Given points are C(2) = 45, C(4) = 143, and C(10) = 869.
Plug them in for C and x to get a system of equations to solve for the constants a, b, and c.
aaaaa wait what
Your points follow the pattern (number of calculator, cost).
$45 to produce 2 calculators means the point is (2, 45).
Plug that into the C(x) equation above.
\[C(x) = ax^2+bx+c\]
You need to do this with the other two data points to get two more equations
Not the answer you are looking for? Search for more explanations.
You need three equations to solve to find the values of the coefficient of x squared (a), the coefficient of x (b), and the numerical term (c) in the quadratic equation that models the cost, c(x).
The three equations are:
45 = 4a + 2b + c ..............(1)
143 = 16a + 4b + c ..........(2)
869 = 100a + 10b + c.......(3)
Subtracting (2) from (1) eliminates c and gives us:
98 = 12a + 2b ...................(4)
And subtracting (2) from (3) gives us:
726 = 84a + 6b = 726 .......(5)
If we multiply (4) by 3 we get:
294 = 36a + 6b .................(6)
And subtracting (6) from (5) eliminates the terms in b and gives us:
432 = 48a ..........................(7)
which enables us to find the value of a to be 9. Plugging the value of a into (6) enables us to find the value of b. The values of a and b can then be plugged into (1) and the value of c can be found.
Finally you can construct the quadratic that models c(x) and find the total cost of producing 7 calculators.