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.
