Complete the blank to summarize what we have seen Doubling o

Complete the blank to summarize what we have seen: Doubling or 2 times C(n) = 2^n - 1 Tripling or 3 times C(n) = 1/3 (3^n - 1) Quadrupling or 4 times C(n) = 1/3 (4^n - 1) Quintupling or 5 times C(n) = (This is your answer to question 10. Following the pattern, what would your closed form expression be if the next day was 12 times the amount of the previous day\'s wage? Dodecatupling or 12 times: C(n) = Complete the boxes and simplify- to show your formula is true. C(n) =

Solution

Sol 11: Observing the C(n) value for 2 times, 3 times and 4 times we can conclude that C(n) for \'a\' times will be=
[aⁿ-1] / [a-1]
Thus for quintupling or five times, C(n) = (  5ⁿ-1) * 1/(5-1)= (5ⁿ-1) /4

Sol 12: For dodecatupling or increasing 12 times C(n) = (12ⁿ-1)* 1/ (12-1) = (12ⁿ-1) / 11
To solve the box:
Thus C(n) = [aⁿ-1] / [a-1] = - [1-aⁿ] / [a-1] = (-1) * (-1) *  [1-aⁿ] / [1-a] = [1-aⁿ] / [1-a]
Thus C(n) = [1-aⁿ] / [1-a] uponc increasing by \'a\' times