A calculator battery loses 3.5% of its sustained charge every month. Assume the charge sustained was 100% when you bought the calculator. How can I write an equation to represent this?

Answer 1

Charge = 100% - 3.5% = 96.5% of the charge left after one month

C = (96.5)^m % where m = number of months

or

y = (.965)^t where y=charge, t=time = number of months

Answer 2

This appears to be an an exponential decay problem. The battery loses 3.5% monthly, or to rewrite that, it retains 100% - 3.5% = 96.5%.

Therefore, the formula is as follows:

Charge = 1 * 0.965^n, where n is the number of months passed.

Simply put: C = 0.965^n

Check:

1 Month = 0.965

2 Month = 0.965 - (0.965 * 0.035) = 0.9312 = 0.965^2