Question

Find the first four iterates of the function f(x) = 2x with an initial value of x0 = 2.

a.
4, 6, 8 ,10
c.
2, 4, 8, 16
b.
2, 4, 6, 8
d.
4, 8, 16, 32


Please select the best answer from the choices provided

Answer 1

d. 4, 8, 16, 32

Explanation:

We'll use the formula f(x) = 2x for each iteration. The output of the first iteration will be come the input of the second iteration, and so on.

So, we start with x0 = 2 and we plug that into the base equation:

x0 = 2 ==> f(x) = 2(2) = 4

x1 = 4 ==> f(x) = 2(4) = 8

x2 = 8 ==> f(x) = 2(2) = 16

x3 = 16 ==> f(x) = 2(2) = 32

x4 = 32 ==> f(x) = 2(2) = 64