Answer:
250 hours
Step-by-step explanation:
The first charge is 10 hours, the second charge is 10(0.96) hours, and so on -- the total of these two is 10+10(0.96) and we need to keep adding our battery usage up until there is no more battery. The third one is 10(0.96)*(0.96), or 10(0.96)².
This can be seen as a geometric series, with 10 as the first tern, or a, and 0.96 as the common ratio, or r. The sum of this is
[tex]a\frac{1-r^{n}}{1-r}[/tex], with n being the number of terms. Since 0.96 to the power of n never actually reaches 0 no matter how high n goes if the number is not infinite, we can say n is infinity. As r^n is really close to 0 when n equals infinity (so close that, for our purposes in this equation, we can just assume it's 0), our equation is then
[tex]10\frac{1}{0.04} =10*25=250[/tex]
