Suppose that a photocopy machine can reduce copies to 70 percent of their original size.

Question

Suppose that a photocopy machine can reduce copies to 70 percent of their original size. By copying an already reduced copy, further reductions can be made.

1) If a page is reduced to 70 percent, what percent enlargement is needed to return it to its original size?

answer =  percent

2) Estimate the number of times in succession that a page must be copied to make the final copy less than 5 percent of the size of the original.

number of times = 

Answer 1

1)

70%/x = 1

So x = 1 / 70% = 1 / 0.70 = 142.86%

2)

5% = 0.05

0.7^x = 0.05

log _0.7 0.05 = x

(log 0.05) / (log 0.7) = 8.4

So 9 times.