Answer:
1548
Step-by-step explanation:
To check your equation lets write out some terms of the sequence
1st month = 1, total in account is 1
2nd month 1 + 1 = 2, total in account is 2
3rd month 2 + 2 = 4, total in account is 4
4th month 4 + 4 = 8, total in account is 8
5th month 8 + 8 = 16, total in account is 16
So the sequence we have is
{1, 1+1, 2 + 2, 4 + 4, 8 + 8,...}→{1, 2, 4, 8, 16,...}
As I see it this is the sequence of partial sums so he does not have 1 + 2 =3 after two months. He did not deposit two dollars for the second month. He only puts enough money in the account to double what was already there. So the summation equation is
st = 2(t - 1), t ≥ 1
Set this equation less than or equal to 1200 and solve for t
1200 ≤ 2(t - 1)
Take the log of each side
log(1200) ≤ log(2(t - 1))
Use the power rule
log(1200) ≤ (t - 1)log(2)
divide each side by log(2) and add 1
log(1200)/log(2) ≤ t - 1
log(1200)/log(2) + 1 ≤ t
t ≥ 11.23, rounding up gives t = 12
so he can contribute to the account for 12 months
At 12 months he has
s12 = 2^11 = 2048, 1024 in account and 1024 that he deposits
What left in the account is 2048 - 500 = 1548
