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

Let n represent number of times battery is charged.

We have been given that 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. We are asked to find the total number of hours the battery can be used over its lifetime.

We can see that our life of battery represents a geometric series, where 1st term is 18 and common ratio is 97% or 0.97.

We will use sum of geometric sequence formula to solve our given problem.

$S_n=\frac{a_1}{1-r}$, where

$S_n$ = Sum of series,

$a_1$ = 1st term

r = Common ratio.

$\frac{18}{1-0.97}=\frac{18}{0.03}=600$

Therefore, the battery can be used for 600 hours over its lifetime.