The table below shows experimental values of $x$ and $y$ which are connected by an equation of t

Question

The table below shows experimental values of $x$ and $y$ which are connected by an equation of the form $y = m^{n+x}$, where $m$ and $n$ are constants. $x$$0.1$$0.2$$0.3$$0.4$$0.5$$0.6$ $y$$5.9$$6.9$$7.2$$9.4$$11.0$$13.1$ Express $y = m^{n+x}$ in a form suitable for drawing a straight line graph, stating clearly the variables that are to be plotted. Using these variables, draw the straight line graph and hence state the correct value of $y$ that is erroneous. Use your graph to estimate the value of $m$ and of $n$. Use your graph to estimate the value of $y$ when $\lg x = -0.456$.

Accepted Answer

(i) Plot $\lg y$ against $x$: $\lg y=x\lg m+n\lg m$. (ii) Replace $7.2$ by approximately $8.1$. (iii) $m\approx5.0,\ n\approx1.0$. (iv) $y\approx8.8$, using the displayed fitted line.

Linear Law - Predictions from Linearised Models

Linear Law - Predictions from Linearised Models

Solution:

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