// Numbas version: exam_results_page_options {"name": "Algebra: exp and log, graphs, solving equations", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra: exp and log, graphs, solving equations", "tags": [], "metadata": {"description": "

\$f(x)= ae^{-bt}+c\$ is given and plotted. A few points are plotted on the curve. \$x\$-coordinates are provided for two of them and \$y\$-coordinate provided for third. Student is required to determine other coordinates.

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This is a calculator question.

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• Remember to check that your answer makes sense, by estimating the coordinates from diagram.
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• See ??
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", "rulesets": {}, "extensions": ["jsxgraph"], "variables": {"f2": {"name": "f2", "group": "part a", "definition": "random(1..(7+c-1))", "description": "", "templateType": "anything"}, "x0": {"name": "x0", "group": "part a", "definition": "1+random(1..9)*0.1", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "part a", "definition": "random(3..10)", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "part a", "definition": "siground(a*e^(b*x0)+c,3)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "part a", "definition": "random(-1..-2)", "description": "", "templateType": "anything"}, "f1": {"name": "f1", "group": "part a", "definition": "siground(a*e^(b*x1)+c,3)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "part a", "definition": "random(-2..-5)", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "part a", "definition": "x0-random(0.1..0.9#0.1)", "description": "", "templateType": "anything"}, "x2": {"name": "x2", "group": "part a", "definition": "siground(ln(((f2-c)/a))/b,3)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "x2<>0", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a", "b", "c", "x0", "f0", "x1", "f1", "x2", "f2"]}], "functions": {"plot": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["x0", "number"], ["y0", "number"], ["x1", "number"], ["y1", "number"], ["x2", "number"], ["y2", "number"]], "type": "html", "language": "javascript", "definition": "// Max and min x and y values for the axis.\nvar x_min = -1;\nvar x_max = 2.5;\nvar y_min = -4;\nvar y_max = 8;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n '500px',\n '600px',\n {\n boundingBox: [x_min,y_max,x_max,y_min],\n axis: false,\n showNavigation: false,\n grid: false,\n axis:false,\n }\n);\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis and y-axis\nvar xaxis = board.create('axis',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,1],{\n// drawLabels: true,\n// label: {offset: [-8, -10]},\n// minorTicks: 0\n//});\n\n// create the y-axis\nvar yaxis = board.create('axis',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\n//var yticks = board.create('ticks',[yaxis,1],{\n// drawLabels: true,\n// label: {offset: [-8, 0]},\n// minorTicks: 0\n//});\n\n\n\n// Plot the function.\n board.create('functiongraph',\n [function(x){ return a*Math.exp(b*x)+c},x_min,x_max]);\n\n// Plot coordinates.\n board.create('ellipse',[[x0,y0+0.045],[x0,y0-0.045],[x0,y0+0.05]],{color:'red'});\n board.create('text',[x0,y0+0.2,'A']);\n board.create('ellipse',[[x1,y1+0.045],[x1,y1-0.045],[x1,y1+0.05]],{color:'red'});\n board.create('text',[x1,y1+0.2,'B']);\n board.create('ellipse',[[x2,y2+0.045],[x2,y2-0.045],[x2,y2+0.05]],{color:'red'});\n board.create('text',[x2,y2+0.2,'C']);\n\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

This is the graph of the function \$f(t) = \\simplify{{a}e^({b}t)+{c}}\$.

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{plot(a,b,c,x0, f0, x1, f1, x2, f2)}

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The \$x\$-coordinate of \$A\$ is \$\\var{x0}\$ and of \$B\$ is \$\\var{x1}\$. The \$y\$-coordinate of \$C\$ is \$\\var{f2}\$.

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Determine the coordinates of \$A,B\$ and \$C\$. Give your answer to 3 s.f..

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Coordinates of A: [[0]]

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Of B: [[1]]

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Of C: [[2]]

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