Maths
posted by Annabella Richards on .
Mrs Smith pays kate for babysitting by giving her 10 cents for the firsthalf hour, 20 cents for the second halfhour, 40 cents for the third halfhour etc. How long does she work to earn $12.70?

1st halfhr = 10 cents = 5*2^1.
2nd halfhr = 20 cents = 5*2^2.
3rd halfhr = 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 halfhrs =
3.99 hrs or 4 hrs.