Agoblin miner earns 1 cent the first day, 2 cents the second day 4 cents the third day, 8 cents the fourth day and so on doubling the amount each day. how much will the miner earn in 7 days ? 2 weeks? 1 month ( make an estimate before solving) show/ explain all work

The easier way to solve this is to make a formula that will calculate number of cents miner earns at day "n"

observing given numbers we can conclude that the formula is:

1 * 2^n

we can see from numbers that they grow very fast which means that the earning/time function is exponential.

sum of first n days is:
a) 7 days
S = 1* (1-2^7)/(1-2) = 127
b) 14 days
S = 1*(1-2^14)/(1-2) = 16383
c) 1 month
will probably get a number with lots of digits
S = 1*(1-2^30)/(1-2) = 1073741824