Questions tagged [exponential]
The exponential tag has no usage guidance.
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Why is a translated exponential function considered an exponential function?
I am tutoring a student preparing to take Calculus 1 at a university. This student hasn't taken precalculus for a year, so I have been drilling him on definitions, rules, and theorems from a college ...
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Method of Solving $5^x=326$ (Logs not allowed)
$5^x=326$
A book titled "algebra and trigonometry" by Paul Foerster, offers this problem. It came before the logarithm chapter and specifically said not to solve with any log manipulation. It ended ...
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Exponential & logarithm in a high school calculus class
So recently I was teaching high school calculus to a high school class and I was wondering about the pedagogically best way to make students actually understand why the derivatives of the exponential &...
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Resource request: 3-4 page review of exponentials and logs
I'm teaching a physics class that has a year of calculus as a prerequisite, but as so often happens, many of my students have forgotten a lot of the much more basic math from earlier classes. In ...
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Natural occurrences of a to the (b to the c)?
Are there some natural contexts in which a double exponential occurs,
$x$ to the ($y$ to the $z$):
$$
x ^ {(y ^ z)} \;, \textrm{or} \;, a ^ {(b ^ c)} \; \textrm{?}
$$
Of course one can contrive many ...
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Project Based Learning (PBL) ideas for secondary math topics
I have searched the web but not found too much that fits what I want. So, I thought I would try asking here.
I am looking for projects to use as PBL for grade 10 math. Specifically for the topics of:
...
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Clearest verb phrases for operations
What is the clearest way to indicate various operations along the following lines:
$f(x) = 3x$: The function $f$ multiplies its input by 3.
$g(x) = x-5$: The function $g$ decreases its input by 5.
$h(...
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Examples for "good" exponential growth versus linear growth
I am writing up a small text about (increasing) exponential functions versus linear functions. I want to make the point that it is not true that if an exponential is bigger than a linear function that ...
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How to explain the "less than yearly compounded interest" concept?
What difficulties can be met while teaching the "less than yearly compounded interest" concept?
Based on my own (learning) experience, an objection arose when I was presented with the formula:
$$A ...
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Interesting settings for exponential growth or decay
If you look for word problems about exponential growth or decay, in text books or on the internet, certain settings arise again and again:
bank accounts,
populations of animals, people or bacteria, ...
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What do the Common Core Standards expect secondary students to learn about logarithms or the number $e$?
I've been looking through the Common Core State Standards (http://www.corestandards.org/Math/) and have been surprised to find very little reference to exponential functions and logarithms. ...
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How can a layperson learn to intuit exponential growth?
I edited and shortened the following's origin. Is learning to intuit exponentiality, implausible (e.g. like hearing Xenakis's gratingly dissonant music as Mozart's tonal consonant melodies)?
Problem ...
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Geometric intuition for $D(e^x) = e^x$
I'm teaching a preparatory course on mathematics at a university. The content is mostly calculus, manipulating expressions and solving equations and inequalities. I show a couple of simple derivations/...
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Motivation for Exponent Rules
I'm going to teach exponentiation to my 7th grade math students, and I like the exponentiation rules to arise in a natural way (through real-world problems or meaningful math problems). Do you have ...