<p>The table below shows experimental values of \(x\) and \(y\) which are connected by an equation of the form \(y = m^{n+x}\), where&nbsp;\(m\) and \(n\) are constants.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">\(x\)</th><th style="text-align: center; --cell-justify: center">\(0.1\)</th><th style="text-align: center; --cell-justify: center">\(0.2\)</th><th style="text-align: center; --cell-justify: center">\(0.3\)</th><th style="text-align: center; --cell-justify: center">\(0.4\)</th><th style="text-align: center; --cell-justify: center">\(0.5\)</th><th style="text-align: center; --cell-justify: center">\(0.6\)</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(y\)</td><td style="text-align: center; --cell-justify: center">\(5.9\)</td><td style="text-align: center; --cell-justify: center">\(6.9\)</td><td style="text-align: center; --cell-justify: center">\(7.2\)</td><td style="text-align: center; --cell-justify: center">\(9.4\)</td><td style="text-align: center; --cell-justify: center">\(11.0\)</td><td style="text-align: center; --cell-justify: center">\(13.1\)</td></tr></tbody></table></div></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Express \(y = m^{n+x}\) in a form suitable for drawing a straight line graph, stating clearly the variables that are to be plotted.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Using these variables, draw the straight line graph and hence state the correct value of \(y\) that is erroneous.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Use your graph to estimate the value of \(m\) and of \(n\).</span></div></li><li><div class="list-item-paragraph">Use your graph to estimate the value of \(y\) when&nbsp;\(\lg x = -0.456\).</div></li></ol>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775549390753-ag7pmkj47wl.png" style="max-width: min(500px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

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.

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 \(\lg x = -0.456\).

Linear Law

Question 73d6a93e