Precalculus question

Question

After each charging, a battery is able to hold only 95% of the charge from the previous charging. The battery was used for 15 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 number of hours of usage between charges forms a geometric series

t_n = rⁿ t₀,

where

t₀ = 15 is the initial period of usage,

t_n is n-th period usage,

r = 0.95 is the rate of change in usage periods.

The infinite sum of this geometric series is

t₀/(1-r) = 15/(1-0.95) = 300 hours