Calculating Remaining Dirt After 11 Passes of a Robot Vacuum

How much dirt will remain after 11 passes of a robot vacuum that removes 18% of the dirt during each pass?

If the floor initially has 590.0ml of dirt, what will be the final amount of dirt remaining after 11 passes?

Final answer:

To find out how much dirt remains after 11 passes of a robot vacuum, we can use the formula for compound interest with the percentage removed as the interest rate and the initial dirt as the principal.

When we use a robot vacuum to clean a dirty floor, it goes through multiple passes to ensure thorough cleaning. During each pass, 18% of the dirt on the floor is removed. If we start with an initial amount of 590.0ml of dirt, we can calculate how much dirt will remain after 11 passes using the formula for compound interest.

The formula for compound interest is:

Remaining Dirt = Initial Dirt × (1 - Percentage Removed) ^ Number of Passes

Substitute the given values into the formula:

Remaining Dirt = 590.0ml × (1 - 0.18) ^ 11

By simplifying this expression, we can determine the final amount of dirt remaining after 11 passes of the robot vacuum.

It is important to understand the process of calculating remaining dirt after multiple passes of a robot vacuum, as it helps in managing cleaning tasks efficiently and effectively.