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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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A B C D
Homework

Video

Solutions for Session 7 Homework

See solutions for Problems: H1 | H2 | H3 | H4 | H5


Problem H1

Here is the completed table. One formula is L = 2,000(0.6)m.

 

Mirror number

 

Reflected light (lumens)

0

 

2,000

1

 

1,200

2

 

720

3

 

432

 

<< back to Problem H1


 

Problem H2

The best way to do this, without using more advanced math such as logarithms, is to continue following the table. This is particularly easy with a spreadsheet. The 10th mirror will reflect about 12 lumens.

<< back to Problem H2


 

Problem H3

We'd be looking for the mirror that reflects closest to 200 lumens, which is the 5th mirror (156 lumens). The 4th mirror reflects 259 lumens; this does not depend on the starting amount of light. This means that the 6th mirror reflects about one-tenth the light of the first mirror, the 7th mirror reflects one-tenth the light of the 2nd mirror, and so on.

<< back to Problem H3


 

Problem H4

a. 

The initial intensity is 1,000 lumens.

b. 

The 1st mirror reflects 700 lumens.

c. 

This fraction is 700 / 1000 = 7/10, or 70 percent.

d. 

Yes, the 2nd mirror appears to reflect about 7/10 of 700 lumens, which is 490 lumens. The 3rd mirror reflects 7/10 of 490 lumens, which is 343 lumens. This pattern appears to continue indefinitely at a constant ratio, so it is an exponential decay situation.

<< back to Problem H4


 

Problem H5

a. 

The outputs keep getting smaller, but remain positive, because at each stage a positive number is divided by 5.

b. 

This is an exponential decay function, because successive outputs are getting smaller, and the base is between 0 and 1.

c. 

Zero will never be an output, even though the outputs will become increasingly close to zero. This happens because the numerator remains 1, no matter what the value of x is, while the denominator becomes increasingly larger as x increases.

d. 

Because two positive numbers are used in the division, a negative number can never result.

e. 

In Problems H1-H4, this implies that even after 100 or more mirrors, some light will still be reflected, although the amount of light reflected will become increasingly small.

<< back to Problem H5

 

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