Give a recursive definition for the set y of all positive multiples of 9. that is, y = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, }. your definition should have a base case and a recursive part.

Recursion means defining something, such as a function, in terms of itself. So Y = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ... }

Let f (0) = 0

So f ( n + 1) = f (n) + 9

f (1) = f(0) + 9 = 0 +9 = 9

f (2) = f(1) + 9 = 9 +9  = 18

Part A
Chorus:
Expontential growth = b*a^x 
b = 15
a = 1.12              (a= r+1), r = 12%

Which gives a function of f(x) = 15*1.12^x 

Band
Linear growth = ax+b
a = 2
b = 30

Which gives a function of g(x)=2x+30

Part B:
f(9) = 15*1.12^9 = 41.59
g(9) = 2*9+30 = 48

Part C:
This is probably problem solving, where you're allowed to use calculators and other softwares.

Therefore you can use different softwares, and make f(x) = g(x).
I did this, and got it to 10.95427141

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