Jerry plans to begin 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. b. b. Jerry plans to keep up this saving pattern until he can no longer afford it. At that time, he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200?
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he amount he deposits is a geometric sequence: 1, 2, 4, 8, 16, ... This is a geometric sequence with a first term of 1 and a common ratio of 2. a = 1 r = 2 The general formula for the sum of the first t terms of a geometric series is: S(t) = a(1 - r^t) / (1 - r) Plug in your values for a and r: S(t) = 1(1 - 2^t) / (1 - 2) S(t) = (1 - 2^t) / -1 S(t) = -1 + 2^t S(t) = 2^t - 1 Answer: S(t) = 2^t - 1 P.S. If he did this for 9 months, he'd have saved $511. P.P.S. If he did this for 2 years, he'd have $16,777,215. P.P.P.S. If he did this for 3 years, he'd have the net worth of Bill Gates at around $70 billion. P.P.P.P.S. If he did this for 4 years, he'd have about $281 trillion. That's enough to give each person in the U.S. about $1 million each. btw im a fast typer and learner
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c. Jerry’s friend Brandon is planning to start saving for a trip at the same time as Jerry. The graph shows the balance in Brandon’s account over the first few months of saving. Whose account will have the greatest balance after the first five months of savings, Brandon’s or Jerry’s?
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