Question

With each cycle, a vacuum pump removes 25% of the air in a glass container. What percent of the air has been removed after 10 cycles?

Answer 1

To calculate the percent of air removed from the container after 10 cycles, we use the formula for exponential decay. After 10 cycles of removing 25% of the air, we calculate the remaining air and then subtract from 100% to find the percent removed.

Step-by-step explanation:

To find out what percent of the air has been removed from a glass container after 10 cycles of a vacuum pump removing 25% of the air each cycle, we can use the formula for exponential decay:

Remaining air = Initial air quantity × (1 - removal rate)number of cycles

In this case, the initial air quantity can be considered 100% (before any removal), the removal rate is 25% or 0.25, and the number of cycles is 10. So:

Remaining air = 100% × (1 - 0.25)10

Calculating the above gives us the remaining air after 10 cycles. To find the percent of air removed, we subtract the remaining air from 100%:

Percent of air removed = 100% - Remaining air.