InterMath | Workshop Support | Write Up Template


Title

Gretelís Goldfish


Problem Statement

Hansel has goldfish that quadruple, or become four times as many, every month. Gretel has goldfish that increase by 20 every month. Right now, Hansel has 4 goldfish and Gretel has 128 goldfish. In how many months will they have the same number of goldfish? Show how you arrived at your answer.


Problem setup

In this problem, I am going to determine in which month Hansel and Gretel will have the same number of goldfish given the fact Hanselís goldfish quadruple each month and Gretelís goldfish increase by 20 each month. I must also consider that Gretel begins with 128 goldfish and Hansel begins with 4.

 

Plans to Solve/Investigate the Problem

In order to solve this problem, I decided to set up an excel spreadsheet. This spreadsheet will enable me to observe the amount of goldfish Hansel and Gretel will have as time passes. From there, I should be able to observe the time that they both have the same amount of goldfish.

 

Investigation/Exploration of the Problem

I set up the spreadsheet by creating a column for Hansel and a column for Gretel. I started the first row with the initial data given in the problem. I set the formula for Hanselís column as times four and Gretalís column as plus 20. Then I copied the formula for both for several months. I noticed that Hanselís number of goldfish increased significantly while Gretelís column had a gradual increase. After evaluating the data, I found that Gretel began with more goldfish but after the third month Hansel had more goldfish than Gretel. This observation led me to realize that sometime between the third and fourth month the data intersected. I then decided to graph the data in order to observe the point of intersection. The following is the data:

Month

Hansel

Gretel

 

1

4

128

-124

2

16

148

-132

3

64

168

-104

4

256

188

68

5

1024

208

816

6

4096

228

3868

7

16384

248

16136

8

65536

268

65268

9

262144

288

261856

10

1048576

308

1048268

The spreadsheet did not pinpoint the point of intersection but when I graphed the data on a line graph I got a much clearer picture of what took place during this time.

 

Extensions of the Problem

Discuss possible extensions for the problem and explore/investigate at least one of the extensions you discussed.

Author & Contact
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U Important Note: You should compose your write-up targeting an audience in mind rather than just the instructor for the course. You are creating a page to publish it on the web.