Posted by **Annabella Richards** on Monday, June 20, 2011 at 2:10am.

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?

- Maths -
**Henry**, Monday, June 20, 2011 at 4:20pm
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.

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