Question

After each charging, a battery is able to hold only 97% of the charge from the previous charging. The battery was used for 18 hours on its first charge before it had to be recharged. What is the total number of hours the battery can be used over its lifetime?

Answer 1

The total nuber of hours that the battery can be used over its lifetime is 600.

Explanation:

We use an infinite geometric series to solve this question.

The sum of all values of an infinite geometric series is given by the following equation:

`S = (a_(1))/(1 - r)`

In which
`a_(1)` is the first term and r is the common ratio.

After each charging, a battery is able to hold only 97% of the charge from the previous charging.

This means that
`r = 0.97`

The battery was used for 18 hours on its first charge before it had to be recharged.

This means that
`a_(1) = 18`

What is the total number of hours the battery can be used over its lifetime?

`S = (18)/(1 - 0.97) = 600`

The total nuber of hours that the battery can be used over its lifetime is 600.