Questions tagged [exponential]

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3
votes
2answers
139 views

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(...
1
vote
4answers
209 views

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 ...
0
votes
2answers
115 views

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 ...
4
votes
0answers
106 views

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 ...
10
votes
5answers
744 views

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, ...
2
votes
1answer
207 views

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 ...
11
votes
1answer
529 views

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. ...
1
vote
1answer
3k views

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: ...
16
votes
12answers
866 views

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/...
7
votes
4answers
4k views

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 ...
8
votes
7answers
873 views

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 ...