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secondary 3 | A Maths
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Hi, could anyone help to answer question 5 with explanation pls? Thank you.
Date Posted: 3 years ago
Views: 136
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For Option 1 , in total you'll be getting 1 million dollars = 100 million cents = 100 000 000 cents
For Option 2, you'll be getting the following :
Day 1 : 1 cent = 2⁰ cent
Day 2 : 2 x 1 cent = 2 cents = 2¹ cents
Day 3 : 2 x 2 cents = 4 cents = 2² cents
Day 4 : 2 x 4 cents = 8 cents = 2³ cents
Day 5 : 2 x 8 cents = 16 cents = 2⁴ cents
This doubling goes on all the way, up to Day 28.
Notice a pattern? The number of cents you get for a particular day is 2⁽ᴰᵃʸ ᴺᵘᵐᵇᵉʳ ⁻ ¹⁾
So, for Day 26, you'll be getting 2²⁶ ⁻ ¹ cents = 2²⁵ cents = 33 554 432 cents
For Day 27, you'll be getting 2²⁷ ⁻ ¹ cents = 2²⁶ cents = 67 108 864 cents
For Day 28, you'll be getting 2²⁸ ⁻ ¹ cents = 2²⁷ cents = 134 217 728 cents
That's 134 million, 217 thousand, 7 hundred and 28 cents, or 134.217728 million dollars
The amount on this last day alone is already more than that lump sum of 1 million dollars in Option 1
Adding all the 28 days up, total you will get = (2⁰ + 2¹ + 2² + 2³ + 2⁴ + ... + 2²⁵ + 2²⁶ + 2²⁷) cents = 268 435 455 cents.
That's more than twice the amount in Option 1 already.
So Option 2 is better since you're getting much more money.
This question demonstrates the power of exponential increases.
For Option 2, you'll be getting the following :
Day 1 : 1 cent = 2⁰ cent
Day 2 : 2 x 1 cent = 2 cents = 2¹ cents
Day 3 : 2 x 2 cents = 4 cents = 2² cents
Day 4 : 2 x 4 cents = 8 cents = 2³ cents
Day 5 : 2 x 8 cents = 16 cents = 2⁴ cents
This doubling goes on all the way, up to Day 28.
Notice a pattern? The number of cents you get for a particular day is 2⁽ᴰᵃʸ ᴺᵘᵐᵇᵉʳ ⁻ ¹⁾
So, for Day 26, you'll be getting 2²⁶ ⁻ ¹ cents = 2²⁵ cents = 33 554 432 cents
For Day 27, you'll be getting 2²⁷ ⁻ ¹ cents = 2²⁶ cents = 67 108 864 cents
For Day 28, you'll be getting 2²⁸ ⁻ ¹ cents = 2²⁷ cents = 134 217 728 cents
That's 134 million, 217 thousand, 7 hundred and 28 cents, or 134.217728 million dollars
The amount on this last day alone is already more than that lump sum of 1 million dollars in Option 1
Adding all the 28 days up, total you will get = (2⁰ + 2¹ + 2² + 2³ + 2⁴ + ... + 2²⁵ + 2²⁶ + 2²⁷) cents = 268 435 455 cents.
That's more than twice the amount in Option 1 already.
So Option 2 is better since you're getting much more money.
This question demonstrates the power of exponential increases.
Thank you so much for your detailed explanation.
Thank you so much for taking the trouble to explain the solution in details.
Welcome
Edit :
The part which stated 134.217728 million dollars was mistyped.
It should be 1.34217728 million instead.
The part which stated 134.217728 million dollars was mistyped.
It should be 1.34217728 million instead.
Thank you once again for taking the trouble to answer my question. I have just posted another Sec3 A Math qn. Wonder if I can trouble you to help me solve it? Thank you so much in advance
Are you able to find my question? Do you need me to type the question here?
I will post later
Hi thank you once again for answering my question. I have posted a Sec4 set language and notation question many days ago but there is no reply. Appreciate if you could help me. Do you want me to type the question or you could search for my qn?
I try to find first.
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