LOGARITHMIC AND EXPONENTIAL EQUATIONS

1
LOGARITHMIC AND EXPONENTIAL EQUATIONS

• REAL-WORLD APPLICATIONS

2
DO NOW

• e(x2) 27. What is the approximate value of
  x?
• 1.30

3
TODAYS OBJECTIVE

• Students will be able to solve real-world
  problems using the number e and logarithmic and
  exponential equations

4
CONTINUOUS INTEREST

• Graphic organizer can be your cheat sheet
• Use e to solve
• 1000 deposited, 15 annual interest rate
• Monthly1160.75, Weekly1161.58,
  Daily1161.80, Continuously1161.83

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SOLVING FOR T

• 5000 entered at rate of 9 annually. How long
  will it take to have 5100 (continuous
  compounding)?
• .22 years (March 21)

6
Solving for R

• Same idea as solving for t
• 190 deposited. You want 250 in the account
  after one year. What interest rate do you need?
• At least 13.88

7
How Are Earthquakes Measured?

• The Richter Scale is logarithmic!!!
• Use this function M.291ln(E) 1.17
• Difference in energy of a 4.1 in Motown vs. 7.1
  in CA?
• 709.4 million ergs!

8
Soups On!

• You all know Newtons Law of Cooling!
• T (Orig. T Room T)e(-rt) Room T
• Cooling rate .046 degrees F/minute. How long
  to a tepid 90 degrees F?
• 42.28 minutes

9
Squirrels

• The formula, APe(rt), is not restricted to
  money.
• Can this be used for population growth?
• Of course! What was the growth rate to have a
  continuous yearly growth from 9700 to 10,000
  squirrels?
• 3

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CLOSURE

• How can you undo an ex function?
• How can you undo a ln function?