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Learning Math Home
Patterns, Functions, and Algebra
 
Session 7 Part A Part B Part C Part D Homework
 
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Session 7 Materials:
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A B C D
Homework

Video

Solutions for Session 7, Part B

See solutions for Problems: B1 |B2 | B3 | B4 | B5 | B6| B7


Problem B1

Most initial reactions are to choose plan A.

<< back to Problem B2


 

Problem B2

The total for 25 weeks of plan A, at $2,000 per week, is $50,000. Plan B, which starts at 1 penny and doubles each week totals $335,544.31, including $167,772.16 in the final week.

solution

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Problem B3

After 40 weeks, the grand total at this job would be $10,995,116,277.75, including just under $5.5 billion in the last week. Before the end of the year, you would exhaust the total money supply of the United States.

<< back to Problem B3


 

Problem B4

Here is the completed table.

 

Years after 1981

 

Estimated Population

0

 

350

1

 

399

2

 

455

3

 

519

4

 

591

5

 

674

 

<< back to Problem B4


 

Problem B5

You can extend the spreadsheet, but an easier way to obtain an answer would be to calculate 350 * (1.14)20 = 4,810 whales. One way to estimate this is to observe that the population seems to be nearly doubling in 5 years (doubling would be 700 whales). This means that we could expect the population to nearly double three more times in a total of 20 years. This doubling would be 350 -> 700 -> 1,400 -> 2,800 -> 5,600, so an estimate is roughly 5,000 whales.

<< back to Problem B5


 

Problem B6

It takes a little more than 5 years. And no, it doesn't matter what the initial population value was, because the ratio of the population after 5 years from now relative to starting population is created only by multiplying 1.14 five times.

<< back to Problem B6


 

Problem B7

One possible pattern is to build, at each stage, a triangle of toothpicks with sides twice as long as the previous triangle.

toothpicks

<< back to Problem B7


 

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