Answer:
The total nuber of hours that the battery can be used over its lifetime is 600.
Step-by-step 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:
[tex]S = \frac{a_{1}}{1 - r}[/tex]
In which [tex]a_{1}[/tex] 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 [tex]r = 0.97[/tex]
The battery was used for 18 hours on its first charge before it had to be recharged.
This means that [tex]a_{1} = 18[/tex]
What is the total number of hours the battery can be used over its lifetime?
[tex]S = \frac{18}{1 - 0.97} = 600[/tex]
The total nuber of hours that the battery can be used over its lifetime is 600.
