The table below shows experimental values of two variables $x$ and $y$. $x$$0.5$$1.5$\(2.5

Question

The table below shows experimental values of two variables $x$ and $y$. $x$$0.5$$1.5$$2.5$$3.5$$4.5$ $y$$12$$30$$74$$185$$463$ It is known that $x$ and $y$ are related by the equation of the form $y^2 = \frac{a^x}{b}$, where $a$ and $b$ are constants. Express this equation in a form suitable for drawing a straight line graph. Using a suitable scale, draw the graph for the given data and use it to estimate the value of $a$ and of $b$. Estimate the value of $x$ for which $\lg \sqrt{y} = 0.7$.

Accepted Answer

(i) $\lg y=\frac{x}{2}\lg a-\frac{1}{2}\lg b$ (ii) $a=6.44$, $b=0.0200$ (iii) $1.35$

Linear Law

Linear Law