Unformatted text preview: ltiply each successive y
term
term
If the multiplier is larger
If
than 1, it’s growth
than
If the multiplier is between
If
0 and 1, it’s decay.
and Exponential growth Exponential decay Exponential Situations
Exponential Money If your savings account earns 3% interest per
If
year, each year you could multiply your
balance by 1.03.
balance
• This is an example of the repeated multiplication. Bacteria Each 42 hours, a bacteria doubles so each 42
Each
hour unit of time, you multiply by 2.
hour
• Another example of repeated multiplication. Exponential Transformation
Exponential The trick is to change the
The
data such that it is linear.
data
This can be done by
This
taking the logarithm.
taking Remember properties of
Remember
logarithms (when you
multiply powers, you add
(linear) exponents)
(linear)
So, essentially, you change
So,
the y values to exponents
the Now look at the new
Now
scatterplot of (x, log y)
scatterplot Years
Years
since
1880
1880 Production in
Production
Millions of
barrels
barrels 0 30 10 77 20 149 30 328 40 428 50 1412 60 2150 Logs of
Barrels
1.477121255
1.886490725
2.173186268
2.515873844
2.631443769
3.149834697
3.3324...
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 Winter '13
 Jessell
 Exponential Function, Exponentiation, Natural logarithm, Logarithm, exponential transformation

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