m Flashcards","topicId":"632c7f96-ee08-4e17-888d-fc88b6c23fa1","topicSlug":"reduction-to-linear-form","cards":[{"id":"f36787f6-b7a8-47b9-a8b3-226fd1976b39","cardType":"basic","front":"For $y=ax^n$, what should be plotted to obtain a straight line?","back":"Plot $\\log y$ against $\\log x$.","points":1,"mcqOptions":null},{"id":"2547d459-8453-4be5-bec3-4f70bb41b981","cardType":"basic","front":"For $y=ax^n$, what does the gradient of a log-log graph represent?","back":"The gradient is $n$.","points":1,"mcqOptions":null},{"id":"09e3825f-e28d-407b-a66d-324e4e52c3b3","cardType":"basic","front":"For $y=ax^n$, what does the vertical intercept of a log-log graph represent?","back":"The intercept is $\\log a$.","points":1,"mcqOptions":null},{"id":"5e8c42af-967c-4bcb-918f-de0718033176","cardType":"basic","front":"For $y=kb^x$, what should be plotted to obtain a straight line?","back":"Plot $\\log y$ against $x$.","points":1,"mcqOptions":null},{"id":"c5d3ed05-b272-44db-89c6-7fa20883b7ac","cardType":"basic","front":"For $y=kb^x$, what does the gradient of the transformed graph represent?","back":"The gradient is $\\log b$.","points":1,"mcqOptions":null},{"id":"338b669e-e22f-4cc0-8d22-c51ed399317b","cardType":"basic","front":"For $y=kb^x$, what does the vertical intercept of the transformed graph represent?","back":"The intercept is $\\log k$.","points":1,"mcqOptions":null},{"id":"cbf61462-1784-4c55-90bb-c7aa5092b64a","cardType":"cloze","front":"For positive $u$ and $v$, $\\text{[...]}$.","back":"For positive $u$ and $v$, $\\boxed{\\log(uv)=\\log u+\\log v}$.","points":null,"mcqOptions":null},{"id":"a190dccb-e964-412e-8b83-acbcf3d220c0","cardType":"cloze","front":"The logarithm power rule is $\\text{[...]}$.","back":"The logarithm power rule is $\\boxed{\\log(u^r)=r\\log u}$.","points":null,"mcqOptions":null},{"id":"620a2c9c-dfad-4489-917c-7e6a8defcf7f","cardType":"cloze","front":"The power model $y=ax^n$ reduces to $\\text{[...]}$.","back":"The power model $y=ax^n$ reduces to $\\boxed{\\log y=n\\log x+\\log a}$.","points":null,"mcqOptions":null},{"id":"6e6d8ea6-2bde-41a7-b47c-e22a019b0371","cardType":"cloze","front":"The exponential model $y=kb^x$ reduces to $\\text{[...]}$.","back":"The exponential model $y=kb^x$ reduces to $\\boxed{\\log y=(\\log b)x+\\log k}$.","points":null,"mcqOptions":null},{"id":"5b60cd25-3942-4bcd-845d-9e7c4eac3612","cardType":"cloze","front":"Using common logarithms, $\\log q=p$ implies $\\text{[...]}$.","back":"Using common logarithms, $\\log q=p$ implies $\\boxed{q=10^p}$.","points":null,"mcqOptions":null},{"id":"71ab2ad2-d233-48cd-b445-f899d45b664c","cardType":"cloze","front":"Using natural logarithms, $\\ln q=p$ implies $\\text{[...]}$.","back":"Using natural logarithms, $\\ln q=p$ implies $\\boxed{q=e^p}$.","points":null,"mcqOptions":null},{"id":"7f1f5883-2ea4-48db-8a78-ced11cc5d156","cardType":"basic","front":"How can you distinguish a power model from an exponential model by the position of $x$?","back":"

Power: $x$ is the base.
Exponential: $x$ is in the exponent.

","points":3,"mcqOptions":null},{"id":"198f139b-e765-4836-ac51-d1ea835187fb","cardType":"basic","front":"If a common-log power graph has intercept $c$, how is $a$ recovered?","back":"Use $a=10^c$.","points":1,"mcqOptions":null},{"id":"b38a85ef-be85-4129-8cea-d1869e567c93","cardType":"basic","front":"If an $\\ln y$ against $x$ graph has intercept $c$, how is $k$ recovered?","back":"Use $k=e^c$.","points":1,"mcqOptions":null},{"id":"af3fd1c3-9b88-4116-b925-c8534634f1a8","cardType":"basic","front":"If an $\\ln y$ against $x$ graph has gradient $m$, how is the exponential base $b$ recovered?","back":"Use $b=e^m$.","points":1,"mcqOptions"

1.6.8 Reduction to linear form Flashcards

1.6.8 Reduction to linear form Flashcards