Question

each time kim pour water from a jug into a glass, exactly 10% of the water remaining in the jug is used. What is the minimum number of times that she must pour water into a glass so that less than half the water remains in thd jug?

Answer 1

The correct answer is:

At least 7 times.

Explanation:

Since 10% of the water in the jug is removed each time, this means that 100-10=90% of the water remains.

After two times, we would have 0.9(0.9) = 0.81 = 81% of the water; each time she pours, the number of times 0.9 is multiplied by itself changes.  This makes this an exponential inequality (it is not an equation, as we want "less than half of the water"):

$0.5 < 0.9^x$

To solve this, we will use logarithms:

$\log_{0.9}(0.5)$