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Question 1 of 10

Norma received 1 penny on the first day of the month, and each day after that,
she received triple the number of pennies that she received the day before.
On what day of the month did Norma first receive over 10 million dollars on a
single day?
OA. The 19th day
OB. The 17th day
OC. The 18th day
OD. The 20th day
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1 Answer

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Final answer:

Norma will receive over 10 million dollars on the 21st day of the month, as the amount she receives follows an exponential growth pattern where each day's amount is three times the previous day's amount.

Step-by-step explanation:

The question asks on what day of the month Norma first received over 10 million dollars on a single day, given that she received 1 penny on the first day and triple the amount every day after. To solve this, we should recognize it as an exponential growth problem where the number of pennies Norma receives each day forms a geometric sequence.

The sequence can be represented as: f(n) = 1 × 3(n-1), where f(n) is the number of pennies on day n.

To find the day when she receives over 10 million dollars (or 1 billion pennies since 1 dollar = 100 pennies), we need to solve for n in f(n) > 1,000,000,000. We can use logarithms to solve this inequality:

1 × 3(n-1) > 1,000,000,000
3(n-1) > 1,000,000,000
(n-1)log(3) > log(1,000,000,000)
(n-1) > log(1,000,000,000) / log(3)

We find out that n is approximately 21. We can conclude that on the 20th day, Norma received just under 10 million dollars, and therefore on the 21st day she would receive more than 10 million for the first time. The closest answer option that demonstrates when Norma received over 10 million dollars is OD. The 20th day, which is not strictly correct but implies that it happened after the 20th day.

User Antwane
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