2.1 Samuel saves two cents the first month and every month later he doubles the amount. How much will he save after two years? a) How much will Samuel save in the 9th month? (5) b) How much will he save after a year and half

a) 33554430 cents

b) 512 cents

c) 524286 cents

Step-by-step explanation:

The savings of Samuel for each month are:

1st month = 2 cents

2nd month = 2*2=2^2=4 cents

3rd month=4*2=2*2*2=2^3=8 cents

4th month=8*2=2*2*2*2=2^4=16 cents

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In general, the savings for the month "n" can be written as:

n month = 2^n cents

a) In two years, we have 24 months. After two years the TOTAL savings will be:

Total = 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... 2^24=33554430 cents=335 544,3$

b) In the 9th month, Samuel will save:

9th month = 2^9 = 512 cents=5,12$

c) In a year and a half, we have 18 months. After a year and a half the TOTAL savings will be:

Total = 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... 2^18=524286 cents = 5242,86$