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Backing out a clean figure

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A count starts at $512$ and grows by $25%$ per period. After $3$ periods, what is it?

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Hint

Write $1.25$ as a fraction and spot the factor $8$ .

Solution

$1.25 = \frac{5}{4}$ , so the factor over $3$ periods is $(\frac{5}{4})^{3} = \frac{125}{64}$ .
$512 \div 64 = 8$ .
So the count is $8 \times 125$ .
The count is $1000$ .

Answer: $1000$