A Goblin 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