Questions tagged [exponential]

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11
votes
5answers
499 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
154 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)? ...
11
votes
1answer
337 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
2k 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
725 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
3k 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 ...
7
votes
7answers
794 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 ...