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MAT_1143-mar_16

MAT_1143-mar_16 - Click to edit Master subtitle style...

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Click to edit Master subtitle style March 16, 2011 5.3-5.4 Exponential Decay and Graphs

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Exponential Growth Our general form Q=C*ax C is initial amount and a is growth factor We only looked at a > 1—growth What if 0 < a < 1? (We NEVER look at a < 0, since neg1/2 gives a problem)
Exponential Decay Say we have a factor of .75 (decay factor) in some situation. Keep 75% of our money (so spend 25%) Y=100*(.75)x Week Keep 75% Avg Rate of Change 0 100.00 \$ 1 75.00 \$ -\$25.00 2 56.25 \$ -\$18.75 3 42.19 \$ -\$14.06 4 31.64 \$ -\$10.55 5 23.73 \$ -\$7.91 6 17.80 \$ -\$5.93 7 13.35 \$ -\$4.45 8 10.01 \$ -\$3.34

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Exponential Decay Say we lose 10% of something For example, scientists might say we lose 10% of facts each month if we don’t review them Our decay factor is 0.90 (what we have left) Month Lose 10% Avg Rate of Change 0 100 1 90 -10.0 2 81 -9.0 3 72.9 -8.1 4 65.61 -7.3 5 59.049 -6.6 6 53.1441 -5.9 7 47.82969 -5.3 8 43.046721 -4.8
A-Decay or B-Growth Y = 0.5*2x Y = 4*0.2x

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Growth/Decay Factor Y = 0.5*2x A. 1 B. 0.5 C. 2 D. 1 Y = 4*0.2x A. 0.2 B. 4 C. 0.8 D. 80%
Initial Value Y = 0.5*2x A. 1 B. 0.5 C. 2 D. 1 Y = 4*0.2x A. 0.2 B. 4 C. 0.8 D. 80%

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Value at a later time?
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