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1
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- Kathy Gross
- Resource: A Mathematics Fantasy
- by Cynthia Lanius
- http://math.rice.edu/~lanius/pro/richte.html
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2
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- You’re sitting in math class,
listening to your teacher intently, when in walks Bill Gates. He offers everyone in the class a job
to help him design the next version of Microsoft Office. He needs everyone for 30 days, and
everyone will have to miss the rest of the semester. The only decision you have to make is
which salary option you would like…
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3
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- The salary options are:
- One cent on the first day, two cents on the second day, and double your
salary every day thereafter for 30 days.
- Exactly $1,000,000!
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4
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- Your friend sitting next to you
jumps at the chance to earn a $1,000,000 and he signs up and is
out the door. He can’t believe
his good fortune.
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5
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- You on the other hand decide to reason this out and decide which option
is better.
- Let’s find out if your friend was smart!
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6
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- Pay with First Option – Week 1
- Day Day’s Pay Total Pay
- 1 .01 .01
- 2 .02 .03
- 3 .04 .07
- 4 .08 .15
- 5 .16 .31
- 6 .32 .63
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7
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- You’ve worked a whole week and
only made $1.27! That’s
discouraging! Do you think you
will ever make a million at this rate?
Fill out the table for the second week and see what you think!
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8
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9
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- At least you are making over
$100 now, but you’re still a long way from $1,000,000. Let’s check out the third week. Fill out your table.
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10
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11
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- You’re getting some serious
money now, over $20,000, but it’s still a long way from a million. You only have 10 days left! What do you think will happen. Is your friend laughing at you
yet? Fill out the fourth table
and let’s see what happens.
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12
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13
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- What’s going on? Look how fast your pay is growing. In
6 days you went from making around $21,000 to over a million. Let’s finish and see what the total
pay will be! Your going to be
rich!
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14
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15
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16
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- Function grows very slowly at first
- Function eventually increases rapidly
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17
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- Option 1 salary represents an exponential function
- Exponential Form: y = bx
- b is the base
- b is > 0 and not equal to 1
- x is a real number
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Notes
