Question

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?

Answer 1

7 times

Explanation:

The formula for this equation would be `V_i/2=V_i*0.9^x`

Dividing both sides by `V_i` gives `0.5=0.9^x`

Taking the log of both sides gives `log(0.5)=xlog(0.9)`

`x=log(0.5)/log(0.9)=6.58...~~7`

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