and logarithms Flashcards","topicId":"2050745c-a980-4b5c-ad4a-2102bb8091e0","topicSlug":"exponentials-and-logarithms-9","cards":[{"id":"8d6d00c9-b943-45f6-878b-72fd76681018","cardType":"cloze","front":"The index laws give $a^m a^n=$ $\\text{[...]}$ and $(a^m)^n=$ $a^{mn}$.","back":"The index laws give $a^m a^n=$ $\\boxed{a^{m+n}}$ and $(a^m)^n=$ $a^{mn}$.","points":null,"mcqOptions":null},{"id":"4ee43fa5-695c-468e-840f-3434d026c922","cardType":"cloze","front":"The index laws give $a^m a^n=$ $a^{m+n}$ and $(a^m)^n=$ $\\text{[...]}$.","back":"The index laws give $a^m a^n=$ $a^{m+n}$ and $(a^m)^n=$ $\\boxed{a^{mn}}$.","points":null,"mcqOptions":null},{"id":"6421735b-4e60-4f3d-a0e4-3e48fd093d3f","cardType":"basic","front":"Rewrite $a^{-n}$ using a positive index.","back":"$a^{-n}=\\frac{1}{a^n}$","points":1,"mcqOptions":null},{"id":"48897f2f-7e65-4d3e-89f8-52c6830fb864","cardType":"cloze","front":"Because $e^x$ and $\\ln x$ are inverses, $\\ln(e^x)=$ $\\text{[...]}$ and $e^{\\ln x}=$ $x$ for $x>0$.","back":"Because $e^x$ and $\\ln x$ are inverses, $\\ln(e^x)=$ $\\boxed{x}$ and $e^{\\ln x}=$ $x$ for $x>0$.","points":null,"mcqOptions":null},{"id":"9686c56d-635b-4daa-b179-0e6ac5fe4de7","cardType":"cloze","front":"Because $e^x$ and $\\ln x$ are inverses, $\\ln(e^x)=$ $x$ and $e^{\\ln x}=$ [ ].","back":"Because $e^x$ and $\\ln x$ are inverses, $\\ln(e^x)=$ $x$ and $e^{\\ln x}=$ $x$ for $x>0$.","points":null,"mcqOptions":null},{"id":"2ef4a4be-721c-4d09-beaa-5bfc492bb803","cardType":"basic","front":"What type of change does $Q=Q_0e^{kt}$ model when $k>0$?","back":"Exponential growth.","points":1,"mcqOptions":null},{"id":"55657f75-c08e-4934-845d-ae202c50ae3c","cardType":"basic","front":"What type of change does $Q=Q_0e^{kt}$ model when $k<0$?","back":"Exponential decay.","points":1,"mcqOptions":null},{"id":"db1ce162-c34e-4448-acf7-12b9c572a7b0","cardType":"basic","front":"Through which point must the graph of $Q=Q_0e^{kt}$ pass?","back":"$(0,Q_0)$","points":1,"mcqOptions":null},{"id":"d4e58f6a-d42d-425c-af73-cb5744ee7e3c","cardType":"basic","front":"Does an exponential decay curve reach zero after a finite time?","back":"No - it approaches zero asymptotically.","points":1,"mcqOptions":null},{"id":"e2b725f5-fec6-4591-a0cd-649481fc8976","cardType":"cloze","front":"For $Q=Q_0e^{kt}$, the magnitude $|k|$ controls [ ], while the units of $k$ must be inverse time units.","back":"For $Q=Q_0e^{kt}$, the magnitude $|k|$ controls how rapidly $Q$ changes, while the units of $k$ must be inverse time units.","points":null,"mcqOptions":null},{"id":"d80e1cc9-51b9-4d99-8be8-d662750d423d","cardType":"cloze","front":"For $Q=Q_0e^{kt}$, the magnitude $|k|$ controls how rapidly $Q$ changes, while the units of $k$ must be [ ].","back":"For $Q=Q_0e^{kt}$, the magnitude $|k|$ controls how rapidly $Q$ changes, while the units of $k$ must be inverse time units.","points":null,"mcqOptions":null},{"id":"eeb487f8-0a37-46f8-9dc8-1068f388849a","cardType":"basic","front":"What differential equation states that the rate of change of $Q$ is proportional to its current value?","back":"$\\frac{dQ}{dt}=kQ$","points":1,"mcqOptions":null},{"id":"5b223bd5-7e3b-4798-be1d-9bfc6c1d0b3c","cardType":"basic","front":"Write the value after $t$ years when

1.5.8 Exponentials and logarithms Flashcards

1.5.8 Exponentials and logarithms Flashcards