Discover

 

A value can increase very quickly when doubled over a period of time. This idea is illustrated in Try This 1.

 

Try This 1

 

Logan asked his father for a weekly allowance. Logan suggested he get one penny the first week and that the allowance double each of the following weeks. Logan’s father thought he should investigate the idea a little further before deciding. He made the following chart:

 

Week	Allowance (cents)	Allowance Written as Base 2
0	1	20 = 1
1	1 × 2 = 2	21 = 2
2	2 × 2 = 4	22 = 4
3	4 × 2 = 8	23 = 8
4	8 × 2 = 16	24 = 16
5
6

1. Complete the rest of the chart. Sketch a graph of allowance (cents) as a function of the week. Describe the shape of the graph.
2. How could you determine the amount of allowance for any specified week?
3. After six weeks Logan would still be receiving less than a dollar per week. Determine the allowance, in dollars, Logan would receive in week 12. (This would be about three months.)

Save your responses in your course folder.

 

Share 1

 

With a partner or group discuss the following question based on the graph you created in Try This 1:

 

Should Logan’s father agree to Logan’s idea for his allowance? Why or why not?

 

If required, save a record of your discussion in your course folder.