Mrs Smith pays kate for babysitting by giving her 10 cents for the first-half hour, 20 cents for the second half-hour, 40 cents for the third half-hour etc. How long does she work to earn $12.70?

Answer 1

1st half-hr = 10 cents = 5*2^1.

2nd half-hr = 20 cents = 5*2^2.

3rd half-hr = 40 cents = 5*2^3.

t = 5*2^n = 1270 cents.
5*2^n = 1270,
Divide both sides by 5:
2^n = 254,
nlog2 = log254,
n = log254 / log2 = 7.99 half-hrs =
3.99 hrs or 4 hrs.