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{"name": "Haifa's new  exponential equation to solve for radioactivity", "extensions": [], "custom_part_types": [], "resources": [["question-resources/pict_1.png", "/srv/numbas/media/question-resources/pict_1.png"], ["question-resources/pict_1_ITOj7zB.png", "/srv/numbas/media/question-resources/pict_1_ITOj7zB.png"], ["question-resources/pict_1_uVwY3Xh.png", "/srv/numbas/media/question-resources/pict_1_uVwY3Xh.png"], ["question-resources/pict_1_KKrpSKi.png", "/srv/numbas/media/question-resources/pict_1_KKrpSKi.png"], ["question-resources/pict_1_H05SCRT.png", "/srv/numbas/media/question-resources/pict_1_H05SCRT.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": "100"}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve an exponential equation for radioactivity</p>"}, "statement": "<p>The radioactivity of fallout <strong>t</strong> days after a nuclear explosion is modeled by&nbsp;<img src=\"resources/question-resources/pict_1_H05SCRT.png\" width=\"150\" height=\"54\"/></p>\n<p>If the radioactivity is found to be&nbsp; \\(1/\\var{2^a}\\) of the original amount after&nbsp;\\(\\var{t}\\) days, find the value of&nbsp;\\(k\\)</p>", "rulesets": {}, "advice": "<p style=\"text-align: center;\">\\(\\var{k}=\\var{a}e^{\\var{m}x+{\\var{c}}}\\)</p>\n<p style=\"text-align: center;\">\\(\\frac{\\var{k}}{\\var{a}}=e^{\\var{m}x+\\var{c}}\\)</p>\n<p style=\"text-align: center;\">\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)=\\var{m}x+\\var{c}\\)</p>\n<p style=\"text-align: center;\">\\(ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}=\\var{m}x\\)</p>\n<p style=\"text-align: center;\">\\(\\frac{ln\\left(\\frac{\\var{k}}{\\var{a}}\\right)-\\var{c}}{\\var{m}}=x\\)</p>", "ungrouped_variables": ["a", "t"], "functions": {}, "name": "Haifa's new  exponential equation to solve for radioactivity", "variables": {"a": {"templateType": "randrange", "name": "a", "description": "", "group": "Ungrouped variables", "definition": "random(1..5#1)"}, "t": {"templateType": "randrange", "name": "t", "description": "", "group": "Ungrouped variables", "definition": "random(2..12#1)"}}, "extensions": [], "tags": [], "preamble": {"css": "", "js": ""}, "parts": [{"prompt": "<p>Input your answer correct to three decimal places.</p>\n<p style=\"padding-left: 30px;\">\\(k = \\) [[0]]</p>", "type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "gaps": [{"checkingaccuracy": 0.001, "scripts": {}, "variableReplacements": [], "answer": "{a}/{t}", "vsetrangepoints": 5, "vsetrange": [0, 1], "checkingtype": "absdiff", "type": "jme", "showCorrectAnswer": true, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "marks": "2", "showpreview": true, "checkvariablenames": false, "showFeedbackIcon": true}], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "variableReplacements": []}], "variable_groups": [], "type": "question", "contributors": [{"name": "haifa abd", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2378/"}]}]}], "contributors": [{"name": "haifa abd", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2378/"}]}