A goblin miner earns 1 cent the first day, 2 cents the second day, 4 cents the third day, 8 cents the fourth day. How much will the miner earn in 30 days?

Ok--I know to double the answer each time until 30--which would be:5,368,709.12
Is there an equation to make this easier?
Thanks

Sort of. Notice that on the nth day, the amount of money that day is 2^(n-1 ) Then notice the amount of money made to date (look at the above figures) is 2^(n-1) -1.

So the total the miner earns in thirty days...

2^29 + 2^29 -1= 2^30 -1 cents.

check that for n= 4, and n=5

Thank you!

You're welcome! It's always good to find patterns and equations to make calculations easier. Just remember to be careful with the exponentiation, as it grows exponentially. If you have any more questions, feel free to ask!

You're welcome! I'm glad I could help. If you have any more questions, feel free to ask!

You're welcome! I'm glad I could help. If you have any more questions, feel free to ask!