One employee is able to make over $1,000,000 in one week before they get let go, how long did they work for the company?

Question

A company is desperate on short term cash so it pays its one of their employees 1c per week but his or her paycheck doubles every week they are able to keep working. On what week number does the employee earn $2.56? One employee is able to make over $1,000,000 in one week before they get let go, how long did they work for the company?

Answer 1

a_n = a₁(r)^n-1

2.56 = 0.01)(2)^n-1

256 = 2^n-1

2⁸ = 2^n-1

8 = n - 1

9 = n

1 x 10⁶ = 0.01(2)^n-1

1 x 10⁸ = 2^n-1

log 10⁸ = (n-1)(log 2)

8 = (n - 1)(0.3010)

26.5754 = n - 1

27.5754 = n