Calculus
Lesson
31
DEs
- Growth and Decay
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A differential equation is an equation with a differential in it!
Examples:
multiply by dx and integrate both sides!
Separable differential equations:
Examples:
Work as general and also solve when you know that the specific
solution goes through the point (2,5).
The most common DE is growth/decay:
work through the problem to get
then
explain
that they can simply write the solution down instead
of working it out each time!
In general,
,
the initial
value (plug in zero for t to check!)
is growth,
is decay
They SHOULD all remember proportionality problems from last year.
Growth/decay problems work the same way!
Examples:
if the interest rate is 5%/year and you start with $100, how much money
do you have after 3 months? After 5 years? Do as both months
and years.
if you have 100 flies after 2 days and 300 flies after 4 days,
how many were there originally?
how long does it take 10g of Pu-239 -> 1g,
if the 1/2 life is 24, 360 years?
Back to Dr. Nandor's Calculus Notes Page
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