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The given function is a quadratic equation. Any quadratic equation can be written in the form :
The given points can be taken as (2,23) ,(4,55) and(10,247)
We form three equations with the given points
For point (2,23 ) the equation is
23 = 4a + 2b + c
For point (4,55) the equation is
55 = 16a + 4b + c
For point (10,247) the equation is:
247 = 100a+10b+c.
Solving the three equations for a,b,c we have :
32 = 12a + 2b
16 = 6a + b
and,
192 = 84 a + 6b
32 = 14a + b
Solving for a,b,c we have:
a=2 b=4 c=7
The quadratic equation is c(x)=
When x=8
c(x)=]
Option C. $167 is the right answer.