Polluting smoke from a power plant loses 15% of its strength for each mile one travels from the plant. How?

Question

far must one go to reduce the strength by 66%. (i.e., 34% of its original strength)?

Answer 1

15% loss is 85% "of" the original (100-15=85)

0.85 * 0.85 = 0.7225 (that's 2 miles)
0.7225 * 0.85 = 0.6141 (3 miles)
0.6141 * 0.85 = 0.5220 (4 miles)
0.5220 * 0.85 = 0.4437 (5 miles)
0.4437 * 0.85 = 0.3771 (6 miles)
0.3771 * 0.85 = 0.3205 (7 miles)
So... somewhere between 6 and 7 miles is 0.3400

In general: 0.85^m = 0.34 gives you 'm' as the exact number of miles. To solve this you take the log of both sides.
log (0.85^m) = log(0.34)
m * log(0.85) = log(0.34)
m * -0.07058 = -0.46852
m = 6.638 miles

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Answer 2

set up a relationship,

1 mile = 15% = 0.15
2 mile = 30% = 0.30
3 mile = 45% = 0.45
4 mile = 60 % = 0.60
5 mile = 75% = 0.75

strenght = 0.15 * distance
.66 = 0.15 * d
d = 0.66/0.15 = 4.4 miles

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Answer 3

No idea. I suck at math.