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Exponential Growth & Decay

These problems explore equations of the form y = ab^{x}. A working knowledge of exponential equations is helpful.
 Related Resources

Interactive resources from our Math Tools project:
Algebra: Exponential Functions
The closest match in our Ask Dr. Math archives:
High School: Exponents
NCTM Standards:
Algebra Standard for Grades 912
Access to these problems requires a Membership.

Ancestors
 Steve Risberg

Algebra, difficulty level 2. Find how many ancestors Gene had from various generations going back
in time.
... more>>

The Bouncing Ball
 Steve Risberg

Algebra, difficulty level 1. A ball is dropped from 27 feet and bounces back to 2/3 of the height
from which it fell. Find and use a formula to calculate the height of
the nth bounce.
... more>>

Cheap Sunglasses
 Steve Risberg

Algebra, difficulty level 2. Help Gilbert figure out if his idea for making cheap sunglasses with
filter film will work.
... more>>

Copying Conundrum
 Annie Fetter

Algebra, difficulty level 1. Using a copy machine, copy an 8 x 10 inch picture at 80%. Then copy the copy at 80%, and repeat this until you have 5 copies of the original. What's the largest dimension now? What's a formula you could use?
... more>>

The Joke
 Steve Risberg

Algebra, difficulty level 1. A joke circulates the Internet via email, with each recipient
forwarding it on to 8 friends. Find a formula to represent the number
of emails sent out at any stage of the forwarding, and use your
formula to answer some questions.
... more>>

Paper and the Moon
 Ethel Breuche

Algebra, difficulty level 4. Students need to express their answers in scientific notation and know how to work in the metric system as well as do conversions to answer this papertearing problem.
... more>>

Sierpinski Stages
 Steve Risberg

Algebra, difficulty level 2. Find and use patterns to determine the total perimeter of an interesting shape.
... more>>

That's Interesting!
 Steve Risberg

Algebra, difficulty level 3. Two men follow different strategies for saving money. Who winds up
with more?
... more>>
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