Question

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

Answer 1

9514 1404 393

Answer:

s(t) = 2^(t-1)

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