Question

Which of the following equations will best fit for the given data?
$\begin{array}{ccccccc}x& 1& 2& 3& 4& 5& 6\\ y& 4& 8& 14& 22& 32& 44\end{array}$

• A. $y=ax+b$
• B. $y=ax+bx+c{x}^2$
• C. $y=e^{ax+b}$
• D. $Noneofthese$

Answer 1

The correct option is B $y=ax+bx+c{x}^2$

At x = 1, y = 4; and x = 2, y = 8
4 = a + b and 8 = 2a + b
$\Rightarrow a=4,b=0$
So, $y=ax+b\Rightarrow y=4x$
The other values do not satisfy this last equation. So option (a) is not fit.
Similarly, we can find that option (c) is also not fit, but option (b) is absolutely fit.