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After opening an ancient bottle you find on the beach, a Genie appears. In payment for his freedom, he gives you a choice either 50,000 gold coins or one magical gold coin. The magical gold coin will turn into two gold coins on the first day. The two coins will turn into four coins total at the end of two days. By the end or the third there will be eight gold coins total. The Genie explains that the magic coins will continue this pattern of doubling each day for one moon cycle, 28 days. Which prize do you choose?
HINT: IT HAS TO DO WITH EXPONENTS
AND PLEASE SHOW YOUR WORK
MAKE A TABLE TOO
I WILL GIVE YOU LOTS OF POINT TOO:)



Answer :

You should choose the prize that gives you more coins. So you just need to figure out what's worth more, the 50,000 or the final amount of magical coins. 

You know that the magical coins double every day. So at the end of 28 days, it will have doubled 28 times (in other words, multiplied by 2, 28 times).

This would be [tex] 2^{28} [/tex] = 268,435,456 (if you just plug it into a calculator). 

If you want to show the amount of magical coins you'd have every day, it would look something like this:

 Day 1 ([tex] 2^{1} [/tex]) : 2 coins
Day 2 ([tex] 2^{2} [/tex]) : 4 coins
Day 3 ([tex] 2^{3} [/tex]) : 8 coins
Day 4 : 16 coins
Day 5 : 32 coins
Day 6 : 64 coins
Day 7 : 128 coins
Day 8 : 256 coins
Day 9 : 512 coins
Day 10 : 1,024 coins
Day 11 : 2,048 coins
Day 12 : 4,096 coins
Day 13 : 8,192 coins
Day 14 : 16,384 coins
Day 15 : 32,768 coins
Day 16 : 65,536 coins
Day 17 : 131,072 coins
Day 18 : 262,144 coins
Day 19 : 524,288 coins
Day 20 : 1,048,576 coins
Day 21 : 2,097,152 coins
Day 22 : 4,194,304 coins
Day 23 : 8,388,608 coins
Day 24 : 16,777,216 coins
Day 25 : 33,554,432 coins
Day 26 : 67,108,864 coins
Day 27 : 134,217,728 coins
Day 28 : 268,435,456 coins

So you'd have more with the magical coin. You should pick the magical coin.

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