Day 34 in
Mat122
Last time
: Began Section 7.4
Next time
: Section 7.7
Today
:
7.3 due Tomorrow
Section 7.4: applications of exponential growth and decay
Exponentials satisfy a very important differential equation:
Doubling time
: the time it takes for a growing exponential function to double in size.
Half life
: the time it takes for a dying exponential function to halve in size.
Forget
The rule of 70 (72, 71, 69.3,...)
:
where
n
is the number of compoundings per year, and
r
is given as a decimal (e.g. 9% is represented by .09).
When compounding is continuous (i.e.
), this reduces to the very lovely rule
Examples:
#9, p. 372
#16, p. 372
#18, p. 372
Section 7.7: L'Hopital's Rule
Now, how do we know that
?
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