Find the total of each option to see which one is better.
Option 1:
$20 every week for 15 weeks = 15 x 20 = $300 total.
Option 2:
Week 1 you have 1 penny.
Week 2 you would have 1 +2 = 3 pennies.
Week 3 you would have 3 + 4 = 7 pennies.
From this we can see a pattern of 2^x - 1 where x is the number of weeks.
So in 15 weeks he would have 2^15 - 1 = 32767 pennies.
100 pennies equal $1
32767 / 100 = $327.67
The second option is better because he ends up with more money.