# Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times a new bar would have to be used so that less than one-half its volume remains?

Oct 18, 2017

7 times

#### Explanation:

The formula for this equation would be ${V}_{i} / 2 = {V}_{i} \cdot {0.9}^{x}$

Dividing both sides by ${V}_{i}$ gives $0.5 = {0.9}^{x}$

Taking the log of both sides gives $\log \left(0.5\right) = x \log \left(0.9\right)$

$x = \log \frac{0.5}{\log} \left(0.9\right) = 6.58 \ldots \approx 7$

It can be used 7 times before less than half of its volume remains.