Jerry plans on saving money for a trip by putting $1 in a savings account the first month and then adding enough to double the amount in the account each following month. Write a function to show how much money Jerry will have in his savings account s (t) after t months

9514 1404 393

  s(t) = 2^(t-1)

Step-by-step explanation:

The amount in the account is the sum of the series ...

  1 + 1 +2 +4 +8 +16 +...

We note that terms after the first are a geometric sequence with a first term 1 and a common ratio 2. The sum of such a sequence is ...

  Sn = a1×(r^n -1)/(r -1) . . . . where n is the number of terms being summed

For our values, this simplifies to ...

  Sn = 1×(2^n -1)/(2 -1) = 2^n -1

We notice here that the account balance is 1 more than this sum, and that n = t-1, so the balance a(t) is ...

  s(t) = 1 +(2^(t -1) -1)

  s(t) = 2^(t -1) . . . . . . the function showing how much Jerry has

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

muyb ajo

step-by-step explanation:

jegosu