and logarithms Flashcards","topicId":"8c44a1f9-f5da-41fa-88c9-4ac619508544","topicSlug":"exponentials-and-logarithms-10","cards":[{"id":"b85f3d37-8435-482d-ae5f-3b841b8350b4","cardType":"cloze","front":"

The product index law is $a^m a^n =$ $\\text{[...]}$.

","back":"

The product index law is $a^m a^n =$ $\\boxed{a^{m+n}}$.

","points":null,"mcqOptions":null},{"id":"bba10aa1-dbc9-4e8d-9961-114735391b09","cardType":"cloze","front":"

A negative index gives $a^{-n} =$ $\\text{[...]}$.

","back":"

A negative index gives $a^{-n} =$ $\\boxed{\\frac{1}{a^n}}$.

","points":null,"mcqOptions":null},{"id":"4ab16b1a-4ed3-4b05-8521-37ca2f74b830","cardType":"basic","front":"

Values at equally spaced times have a constant ratio. What type of model is indicated?

","back":"

An exponential model.

","points":1,"mcqOptions":null},{"id":"34147749-6805-45eb-8e5f-64873638e130","cardType":"basic","front":"

Why is $A$ the initial value in $Q=Ab^t$?

","back":"

At $t=0$, $b^0=1$, so $Q=A$.

","points":2,"mcqOptions":null},{"id":"d3dae66b-af31-4d74-a8e0-148700617df2","cardType":"cloze","front":"

An increase of $r$% gives the multiplier $\\text{[...]}$.

","back":"

An increase of $r$% gives the multiplier $\\boxed{1+\\frac{r}{100}}$.

","points":null,"mcqOptions":null},{"id":"3e271d12-821c-479a-92f6-d5913d00c2d2","cardType":"cloze","front":"

A decrease of $r$% gives the multiplier $\\text{[...]}$.

","back":"

A decrease of $r$% gives the multiplier $\\boxed{1-\\frac{r}{100}}$.

","points":null,"mcqOptions":null},{"id":"93dd831b-5d5e-42b4-89d0-d67b15e61acd","cardType":"basic","front":"

What condition on $b$ makes $Q=Ab^t$ a growth model?

","back":"

$b>1$.

","points":1,"mcqOptions":null},{"id":"e3af18f4-38dd-4298-b183-92961c4fd8f4","cardType":"basic","front":"

What condition on $b$ makes $Q=Ab^t$ a decay model?

","back":"

$0<b<1$.

","points":1,"mcqOptions":null},{"id":"e35c49ea-b448-424a-a3a3-6c812bac8963","cardType":"basic","front":"

What is the horizontal asymptote of a positive exponential decay model?

","back":"

$Q=0$.

","points":1,"mcqOptions":null},{"id":"f782ab51-4946-43c1-ac62-c3973cc35732","cardType":"cloze","front":"

In $Q=Ae^{kt}$, continuous growth requires $\\text{[...]}$.

","back":"

In $Q=Ae^{kt}$, continuous growth requires $\\boxed{k>0}$.

","points":null,"mcqOptions":null},{"id":"8e3c5ddc-17c4-410c-acd2-4bfb0bbe461a","cardType":"cloze","front":"

In $Q=Ae^{kt}$, continuous decay requires $\\text{[...]}$.

","back":"

In $Q=Ae^{kt}$, continuous decay requires $\\boxed{k<0}$.

","points":null,"mcqOptions":null},{"id":"e6f4361a-d4db-4771-a76e-aaf09410bce5","cardType":"basic","front":"

If $t$ is measured in years, what are the units of $k$ in $Q=Ae^{kt}$?

","back":"

Per year.

","points":1,"mcqOptions":null},{"id":"19aad4b6-5c50-4744-a3e5-2d8fc4ae3e4d","cardType":"basic","front":"

Why does $e^{kt}$ occur naturally in continuous growth and decay models?

","back":"

Its rate of change is proportional to its current value.

","points":2,"mcqOptions":null},{"id":"886724f5-a4ce-48bf-bd1b-a84309b8898f","cardType":"basic","front":"

Which model gives the value of principal $P$ after $t$ years at continuously compounded rate $r$?

","back":"

$V=Pe^{rt}$.

","points":1,"mcqOptions":null},{"id":"748ad7a9-048a-4404-9521-3cab85af8ec2","cardType":"basic","front":"

Why does $C=C_0e^{-kt}$ decrease when $k>0$?

","back":"

The negative exponent makes the exponential factor decrease with time.

","points":2,"mcqOptions":null},{"id":"4ae40295-7b27-4ff6-b38a-3cf34f6d60bb","cardType":"basic","front":"

How does $Q=Q_0\\left(\\frac12\\right)^{t/h}$ account for a partial half-life?

","back":"

The exponent $t/h$ can be non-integer.

","points":2,"mcqOptions":null},{"id":"310dea82-ebbc-4d3f-9dc3-739d3069cb07","cardType":"basic","front":"

1.6.9 Exponentials and logarithms Flashcards

1.6.9 Exponentials and logarithms Flashcards