Student Activity with
 Exponents
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Here's a problem which may demonstrate the usefulness of exponents to your students.

Pose this problem to the class and give them 10 or 15 minutes to come up with an answer they can prove is valid.  Most of the students will probably use a calculator and figure the answer by continually multiplying by 2.  If none of the students comes up with the shorter way, you can show them how easy the use of exponents makes the solution !

 

 

The Problem Statement
   

Richie Rich celebrates his birthday on June 1.  This year, his parents have given him his choice of gifts.  He can choose one of the following options:
 

Option 1

His parents will give him $500,000 on June 1.

 

Option 2

His parents will deposit $2 in a savings account on June 1.  Each day they will double the amount in that account until the end of the month.  On June 30, Richie can have whatever money has accumulated in the account.
 

Ask the students which option they would choose.  If they choose
option 1, they end up with $500,000, but option 2 yields $230
 or $1,073,741,824.

Account Balance

Day 1

$2

Day 2

$4

Day 3

$8

Day 4

$16

Day 5

$32

Day 6

$64

Day 7

$128

Day 8

$256

Day 9

$512

Day 10

$1,024

Day 11

$2,048

Day 12

$4,096

Day 13

$8,192

Day 14

$16,384

Day 15

$32,768

Day 16

$65,536

Day 17

$131,072

Day 18

$262,144

Day 19

$524,288

Day 20

$1,048,576

Day 21

$2,097,152

Day 22

$4,194,304

Day 23

$8,388,608

Day 24

$16,777,216

Day 25

$33,554,432

Day 26

$67,108,864

Day 27

$134,217,728

Day 28

$268,435,456

Day 29

$536,870,912

Day 30

$1,073,741,824