If you invest x dollars at 6% interest compounded annually, then the amount a(x) of the investment after one year is a(x) = 1.06x. find a ○ a, a ○ a ○ a, and a ○ a ○ a ○ a. what do these compositions represent?

Step-by-step explanation:

The composition A ○ A is equivalent to A(A(x)) which is the amount of the investment one year after the original amount matured (at one year). That is, it is the amount of the investment after 2 years. Its value is ...

  A(A(x)) = 1.06(1.06x) = 1.06²x

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Similarly, ...

  A ○ A ○ A = A(A(A(x))) = 1.06(1.06(1.06x)) = 1.06³x, and

  A ○ A ○ A ○ A = A(A(A(A(x = 1.06(1.06³x) = 1.06⁴x

These are the amounts after 3 and 4 years, respectively.

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.